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Simplifying -1(3x + -5) + -1(11x + -6) + 4 = -14(x + -1) * 1(4x + 14) + 3 Reorder the terms: -1(-5 + 3x) + -1(11x + -6) + 4 = -14(x + -1) * 1(4x + 14) + 3 (-5 * -1 + 3x * -1) + -1(11x + -6) + 4 = -14(x + -1) * 1(4x + 14) + 3 (5 + -3x) + -1(11x + -6) + 4 = -14(x + -1) * 1(4x + 14) + 3 Reorder the terms: 5 + -3x + -1(-6 + 11x) + 4 = -14(x + -1) * 1(4x + 14) + 3 5 + -3x + (-6 * -1 + 11x * -1) + 4 = -14(x + -1) * 1(4x + 14) + 3 5 + -3x + (6 + -11x) + 4 = -14(x + -1) * 1(4x + 14) + 3 Reorder the terms: 5 + 6 + 4 + -3x + -11x = -14(x + -1) * 1(4x + 14) + 3 Combine like terms: 5 + 6 = 11 11 + 4 + -3x + -11x = -14(x + -1) * 1(4x + 14) + 3 Combine like terms: 11 + 4 = 15 15 + -3x + -11x = -14(x + -1) * 1(4x + 14) + 3 Combine like terms: -3x + -11x = -14x 15 + -14x = -14(x + -1) * 1(4x + 14) + 3 Reorder the terms: 15 + -14x = -14(-1 + x) * 1(4x + 14) + 3 Reorder the terms: 15 + -14x = -14(-1 + x) * 1(14 + 4x) + 3 Reorder the terms for easier multiplication: 15 + -14x = -14 * 1(-1 + x)(14 + 4x) + 3 Multiply -14 * 1 15 + -14x = -14(-1 + x)(14 + 4x) + 3 Multiply (-1 + x) * (14 + 4x) 15 + -14x = -14(-1(14 + 4x) + x(14 + 4x)) + 3 15 + -14x = -14((14 * -1 + 4x * -1) + x(14 + 4x)) + 3 15 + -14x = -14((-14 + -4x) + x(14 + 4x)) + 3 15 + -14x = -14(-14 + -4x + (14 * x + 4x * x)) + 3 15 + -14x = -14(-14 + -4x + (14x + 4x2)) + 3 Combine like terms: -4x + 14x = 10x 15 + -14x = -14(-14 + 10x + 4x2) + 3 15 + -14x = (-14 * -14 + 10x * -14 + 4x2 * -14) + 3 15 + -14x = (196 + -140x + -56x2) + 3 Reorder the terms: 15 + -14x = 196 + 3 + -140x + -56x2 Combine like terms: 196 + 3 = 199 15 + -14x = 199 + -140x + -56x2 Solving 15 + -14x = 199 + -140x + -56x2 Solving for variable 'x'. Reorder the terms: 15 + -199 + -14x + 140x + 56x2 = 199 + -140x + -56x2 + -199 + 140x + 56x2 Combine like terms: 15 + -199 = -184 -184 + -14x + 140x + 56x2 = 199 + -140x + -56x2 + -199 + 140x + 56x2 Combine like terms: -14x + 140x = 126x -184 + 126x + 56x2 = 199 + -140x + -56x2 + -199 + 140x + 56x2 Reorder the terms: -184 + 126x + 56x2 = 199 + -199 + -140x + 140x + -56x2 + 56x2 Combine like terms: 199 + -199 = 0 -184 + 126x + 56x2 = 0 + -140x + 140x + -56x2 + 56x2 -184 + 126x + 56x2 = -140x + 140x + -56x2 + 56x2 Combine like terms: -140x + 140x = 0 -184 + 126x + 56x2 = 0 + -56x2 + 56x2 -184 + 126x + 56x2 = -56x2 + 56x2 Combine like terms: -56x2 + 56x2 = 0 -184 + 126x + 56x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-92 + 63x + 28x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-92 + 63x + 28x2)' equal to zero and attempt to solve: Simplifying -92 + 63x + 28x2 = 0 Solving -92 + 63x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -3.285714286 + 2.25x + x2 = 0 Move the constant term to the right: Add '3.285714286' to each side of the equation. -3.285714286 + 2.25x + 3.285714286 + x2 = 0 + 3.285714286 Reorder the terms: -3.285714286 + 3.285714286 + 2.25x + x2 = 0 + 3.285714286 Combine like terms: -3.285714286 + 3.285714286 = 0.000000000 0.000000000 + 2.25x + x2 = 0 + 3.285714286 2.25x + x2 = 0 + 3.285714286 Combine like terms: 0 + 3.285714286 = 3.285714286 2.25x + x2 = 3.285714286 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 3.285714286 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 3.285714286 + 1.265625 Combine like terms: 3.285714286 + 1.265625 = 4.551339286 1.265625 + 2.25x + x2 = 4.551339286 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 4.551339286 Calculate the square root of the right side: 2.133386811 Break this problem into two subproblems by setting (x + 1.125) equal to 2.133386811 and -2.133386811.Subproblem 1
x + 1.125 = 2.133386811 Simplifying x + 1.125 = 2.133386811 Reorder the terms: 1.125 + x = 2.133386811 Solving 1.125 + x = 2.133386811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 2.133386811 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 2.133386811 + -1.125 x = 2.133386811 + -1.125 Combine like terms: 2.133386811 + -1.125 = 1.008386811 x = 1.008386811 Simplifying x = 1.008386811Subproblem 2
x + 1.125 = -2.133386811 Simplifying x + 1.125 = -2.133386811 Reorder the terms: 1.125 + x = -2.133386811 Solving 1.125 + x = -2.133386811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -2.133386811 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -2.133386811 + -1.125 x = -2.133386811 + -1.125 Combine like terms: -2.133386811 + -1.125 = -3.258386811 x = -3.258386811 Simplifying x = -3.258386811Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.008386811, -3.258386811}Solution
x = {1.008386811, -3.258386811}
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