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Simplifying 2x + 8x + -16x * 89x + -34x + 89 = 0 Reorder the terms for easier multiplication: 2x + 8x + -16 * 89x * x + -34x + 89 = 0 Multiply -16 * 89 2x + 8x + -1424x * x + -34x + 89 = 0 Multiply x * x 2x + 8x + -1424x2 + -34x + 89 = 0 Reorder the terms: 89 + 2x + 8x + -34x + -1424x2 = 0 Combine like terms: 2x + 8x = 10x 89 + 10x + -34x + -1424x2 = 0 Combine like terms: 10x + -34x = -24x 89 + -24x + -1424x2 = 0 Solving 89 + -24x + -1424x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1424 the coefficient of the squared term: Divide each side by '-1424'. -0.0625 + 0.01685393258x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 0.01685393258x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 0.01685393258x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 0.01685393258x + x2 = 0 + 0.0625 0.01685393258x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 0.01685393258x + x2 = 0.0625 The x term is 0.01685393258x. Take half its coefficient (0.00842696629). Square it (0.00007101376085) and add it to both sides. Add '0.00007101376085' to each side of the equation. 0.01685393258x + 0.00007101376085 + x2 = 0.0625 + 0.00007101376085 Reorder the terms: 0.00007101376085 + 0.01685393258x + x2 = 0.0625 + 0.00007101376085 Combine like terms: 0.0625 + 0.00007101376085 = 0.06257101376085 0.00007101376085 + 0.01685393258x + x2 = 0.06257101376085 Factor a perfect square on the left side: (x + 0.00842696629)(x + 0.00842696629) = 0.06257101376085 Calculate the square root of the right side: 0.250141987 Break this problem into two subproblems by setting (x + 0.00842696629) equal to 0.250141987 and -0.250141987.Subproblem 1
x + 0.00842696629 = 0.250141987 Simplifying x + 0.00842696629 = 0.250141987 Reorder the terms: 0.00842696629 + x = 0.250141987 Solving 0.00842696629 + x = 0.250141987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00842696629' to each side of the equation. 0.00842696629 + -0.00842696629 + x = 0.250141987 + -0.00842696629 Combine like terms: 0.00842696629 + -0.00842696629 = 0.00000000000 0.00000000000 + x = 0.250141987 + -0.00842696629 x = 0.250141987 + -0.00842696629 Combine like terms: 0.250141987 + -0.00842696629 = 0.24171502071 x = 0.24171502071 Simplifying x = 0.24171502071Subproblem 2
x + 0.00842696629 = -0.250141987 Simplifying x + 0.00842696629 = -0.250141987 Reorder the terms: 0.00842696629 + x = -0.250141987 Solving 0.00842696629 + x = -0.250141987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00842696629' to each side of the equation. 0.00842696629 + -0.00842696629 + x = -0.250141987 + -0.00842696629 Combine like terms: 0.00842696629 + -0.00842696629 = 0.00000000000 0.00000000000 + x = -0.250141987 + -0.00842696629 x = -0.250141987 + -0.00842696629 Combine like terms: -0.250141987 + -0.00842696629 = -0.25856895329 x = -0.25856895329 Simplifying x = -0.25856895329Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.24171502071, -0.25856895329}
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