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Simplifying 10x(x + -2) + 15 = 8x + 7 Reorder the terms: 10x(-2 + x) + 15 = 8x + 7 (-2 * 10x + x * 10x) + 15 = 8x + 7 (-20x + 10x2) + 15 = 8x + 7 Reorder the terms: 15 + -20x + 10x2 = 8x + 7 Reorder the terms: 15 + -20x + 10x2 = 7 + 8x Solving 15 + -20x + 10x2 = 7 + 8x Solving for variable 'x'. Reorder the terms: 15 + -7 + -20x + -8x + 10x2 = 7 + 8x + -7 + -8x Combine like terms: 15 + -7 = 8 8 + -20x + -8x + 10x2 = 7 + 8x + -7 + -8x Combine like terms: -20x + -8x = -28x 8 + -28x + 10x2 = 7 + 8x + -7 + -8x Reorder the terms: 8 + -28x + 10x2 = 7 + -7 + 8x + -8x Combine like terms: 7 + -7 = 0 8 + -28x + 10x2 = 0 + 8x + -8x 8 + -28x + 10x2 = 8x + -8x Combine like terms: 8x + -8x = 0 8 + -28x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -14x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -14x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + -14x + 5x2 = 0 Solving 4 + -14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + -2.8x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -2.8x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -2.8x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -2.8x + x2 = 0 + -0.8 -2.8x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -2.8x + x2 = -0.8 The x term is -2.8x. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8x + 1.96 + x2 = -0.8 + 1.96 Reorder the terms: 1.96 + -2.8x + x2 = -0.8 + 1.96 Combine like terms: -0.8 + 1.96 = 1.16 1.96 + -2.8x + x2 = 1.16 Factor a perfect square on the left side: (x + -1.4)(x + -1.4) = 1.16 Calculate the square root of the right side: 1.077032961 Break this problem into two subproblems by setting (x + -1.4) equal to 1.077032961 and -1.077032961.Subproblem 1
x + -1.4 = 1.077032961 Simplifying x + -1.4 = 1.077032961 Reorder the terms: -1.4 + x = 1.077032961 Solving -1.4 + x = 1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = 1.077032961 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = 1.077032961 + 1.4 x = 1.077032961 + 1.4 Combine like terms: 1.077032961 + 1.4 = 2.477032961 x = 2.477032961 Simplifying x = 2.477032961Subproblem 2
x + -1.4 = -1.077032961 Simplifying x + -1.4 = -1.077032961 Reorder the terms: -1.4 + x = -1.077032961 Solving -1.4 + x = -1.077032961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + x = -1.077032961 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + x = -1.077032961 + 1.4 x = -1.077032961 + 1.4 Combine like terms: -1.077032961 + 1.4 = 0.322967039 x = 0.322967039 Simplifying x = 0.322967039Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.477032961, 0.322967039}Solution
x = {2.477032961, 0.322967039}
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