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Simplifying 4(-3x + 1) = -10x(x + -4) + -14x Reorder the terms: 4(1 + -3x) = -10x(x + -4) + -14x (1 * 4 + -3x * 4) = -10x(x + -4) + -14x (4 + -12x) = -10x(x + -4) + -14x Reorder the terms: 4 + -12x = -10x(-4 + x) + -14x 4 + -12x = (-4 * -10x + x * -10x) + -14x 4 + -12x = (40x + -10x2) + -14x Reorder the terms: 4 + -12x = 40x + -14x + -10x2 Combine like terms: 40x + -14x = 26x 4 + -12x = 26x + -10x2 Solving 4 + -12x = 26x + -10x2 Solving for variable 'x'. Combine like terms: -12x + -26x = -38x 4 + -38x + 10x2 = 26x + -10x2 + -26x + 10x2 Reorder the terms: 4 + -38x + 10x2 = 26x + -26x + -10x2 + 10x2 Combine like terms: 26x + -26x = 0 4 + -38x + 10x2 = 0 + -10x2 + 10x2 4 + -38x + 10x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 4 + -38x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -19x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -19x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + -19x + 5x2 = 0 Solving 2 + -19x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -3.8x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -3.8x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -3.8x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -3.8x + x2 = 0 + -0.4 -3.8x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -3.8x + x2 = -0.4 The x term is -3.8x. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8x + 3.61 + x2 = -0.4 + 3.61 Reorder the terms: 3.61 + -3.8x + x2 = -0.4 + 3.61 Combine like terms: -0.4 + 3.61 = 3.21 3.61 + -3.8x + x2 = 3.21 Factor a perfect square on the left side: (x + -1.9)(x + -1.9) = 3.21 Calculate the square root of the right side: 1.791647287 Break this problem into two subproblems by setting (x + -1.9) equal to 1.791647287 and -1.791647287.Subproblem 1
x + -1.9 = 1.791647287 Simplifying x + -1.9 = 1.791647287 Reorder the terms: -1.9 + x = 1.791647287 Solving -1.9 + x = 1.791647287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = 1.791647287 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = 1.791647287 + 1.9 x = 1.791647287 + 1.9 Combine like terms: 1.791647287 + 1.9 = 3.691647287 x = 3.691647287 Simplifying x = 3.691647287Subproblem 2
x + -1.9 = -1.791647287 Simplifying x + -1.9 = -1.791647287 Reorder the terms: -1.9 + x = -1.791647287 Solving -1.9 + x = -1.791647287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = -1.791647287 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = -1.791647287 + 1.9 x = -1.791647287 + 1.9 Combine like terms: -1.791647287 + 1.9 = 0.108352713 x = 0.108352713 Simplifying x = 0.108352713Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.691647287, 0.108352713}Solution
x = {3.691647287, 0.108352713}
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