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Simplifying 5 + (8x + -12) * 4x = -1x Reorder the terms: 5 + (-12 + 8x) * 4x = -1x Reorder the terms for easier multiplication: 5 + 4x(-12 + 8x) = -1x 5 + (-12 * 4x + 8x * 4x) = -1x 5 + (-48x + 32x2) = -1x Solving 5 + -48x + 32x2 = -1x Solving for variable 'x'. Reorder the terms: 5 + -48x + x + 32x2 = -1x + x Combine like terms: -48x + x = -47x 5 + -47x + 32x2 = -1x + x Combine like terms: -1x + x = 0 5 + -47x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.15625 + -1.46875x + x2 = 0 Move the constant term to the right: Add '-0.15625' to each side of the equation. 0.15625 + -1.46875x + -0.15625 + x2 = 0 + -0.15625 Reorder the terms: 0.15625 + -0.15625 + -1.46875x + x2 = 0 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + -1.46875x + x2 = 0 + -0.15625 -1.46875x + x2 = 0 + -0.15625 Combine like terms: 0 + -0.15625 = -0.15625 -1.46875x + x2 = -0.15625 The x term is -1.46875x. Take half its coefficient (-0.734375). Square it (0.5393066406) and add it to both sides. Add '0.5393066406' to each side of the equation. -1.46875x + 0.5393066406 + x2 = -0.15625 + 0.5393066406 Reorder the terms: 0.5393066406 + -1.46875x + x2 = -0.15625 + 0.5393066406 Combine like terms: -0.15625 + 0.5393066406 = 0.3830566406 0.5393066406 + -1.46875x + x2 = 0.3830566406 Factor a perfect square on the left side: (x + -0.734375)(x + -0.734375) = 0.3830566406 Calculate the square root of the right side: 0.618915697 Break this problem into two subproblems by setting (x + -0.734375) equal to 0.618915697 and -0.618915697.Subproblem 1
x + -0.734375 = 0.618915697 Simplifying x + -0.734375 = 0.618915697 Reorder the terms: -0.734375 + x = 0.618915697 Solving -0.734375 + x = 0.618915697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.734375' to each side of the equation. -0.734375 + 0.734375 + x = 0.618915697 + 0.734375 Combine like terms: -0.734375 + 0.734375 = 0.000000 0.000000 + x = 0.618915697 + 0.734375 x = 0.618915697 + 0.734375 Combine like terms: 0.618915697 + 0.734375 = 1.353290697 x = 1.353290697 Simplifying x = 1.353290697Subproblem 2
x + -0.734375 = -0.618915697 Simplifying x + -0.734375 = -0.618915697 Reorder the terms: -0.734375 + x = -0.618915697 Solving -0.734375 + x = -0.618915697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.734375' to each side of the equation. -0.734375 + 0.734375 + x = -0.618915697 + 0.734375 Combine like terms: -0.734375 + 0.734375 = 0.000000 0.000000 + x = -0.618915697 + 0.734375 x = -0.618915697 + 0.734375 Combine like terms: -0.618915697 + 0.734375 = 0.115459303 x = 0.115459303 Simplifying x = 0.115459303Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.353290697, 0.115459303}
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