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Simplifying x(5x + -4) + x(3x + -2) = 23 + -10 Reorder the terms: x(-4 + 5x) + x(3x + -2) = 23 + -10 (-4 * x + 5x * x) + x(3x + -2) = 23 + -10 (-4x + 5x2) + x(3x + -2) = 23 + -10 Reorder the terms: -4x + 5x2 + x(-2 + 3x) = 23 + -10 -4x + 5x2 + (-2 * x + 3x * x) = 23 + -10 -4x + 5x2 + (-2x + 3x2) = 23 + -10 Reorder the terms: -4x + -2x + 5x2 + 3x2 = 23 + -10 Combine like terms: -4x + -2x = -6x -6x + 5x2 + 3x2 = 23 + -10 Combine like terms: 5x2 + 3x2 = 8x2 -6x + 8x2 = 23 + -10 Combine like terms: 23 + -10 = 13 -6x + 8x2 = 13 Solving -6x + 8x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -6x + 8x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -6x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + -0.75x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + -0.75x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + -0.75x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + -0.75x + x2 = 0 + 1.625 -0.75x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 -0.75x + x2 = 1.625 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 1.625 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 1.625 + 0.140625 Combine like terms: 1.625 + 0.140625 = 1.765625 0.140625 + -0.75x + x2 = 1.765625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x + -0.375) equal to 1.328768227 and -1.328768227.Subproblem 1
x + -0.375 = 1.328768227 Simplifying x + -0.375 = 1.328768227 Reorder the terms: -0.375 + x = 1.328768227 Solving -0.375 + x = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.328768227 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.328768227 + 0.375 x = 1.328768227 + 0.375 Combine like terms: 1.328768227 + 0.375 = 1.703768227 x = 1.703768227 Simplifying x = 1.703768227Subproblem 2
x + -0.375 = -1.328768227 Simplifying x + -0.375 = -1.328768227 Reorder the terms: -0.375 + x = -1.328768227 Solving -0.375 + x = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.328768227 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.328768227 + 0.375 x = -1.328768227 + 0.375 Combine like terms: -1.328768227 + 0.375 = -0.953768227 x = -0.953768227 Simplifying x = -0.953768227Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.703768227, -0.953768227}
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