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Simplifying x + 155x(-1x) = 12 Remove parenthesis around (-1x) x + 155x * -1x = 12 Reorder the terms for easier multiplication: x + 155 * -1x * x = 12 Multiply 155 * -1 x + -155x * x = 12 Multiply x * x x + -155x2 = 12 Solving x + -155x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + x + -155x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + x + -155x2 = 0 Begin completing the square. Divide all terms by -155 the coefficient of the squared term: Divide each side by '-155'. 0.07741935484 + -0.006451612903x + x2 = 0 Move the constant term to the right: Add '-0.07741935484' to each side of the equation. 0.07741935484 + -0.006451612903x + -0.07741935484 + x2 = 0 + -0.07741935484 Reorder the terms: 0.07741935484 + -0.07741935484 + -0.006451612903x + x2 = 0 + -0.07741935484 Combine like terms: 0.07741935484 + -0.07741935484 = 0.00000000000 0.00000000000 + -0.006451612903x + x2 = 0 + -0.07741935484 -0.006451612903x + x2 = 0 + -0.07741935484 Combine like terms: 0 + -0.07741935484 = -0.07741935484 -0.006451612903x + x2 = -0.07741935484 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.006451612903x + 0.25 + x2 = -0.07741935484 + 0.25 Reorder the terms: 0.25 + -0.006451612903x + x2 = -0.07741935484 + 0.25 Combine like terms: -0.07741935484 + 0.25 = 0.17258064516 0.25 + -0.006451612903x + x2 = 0.17258064516 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.17258064516 Calculate the square root of the right side: 0.415428267 Break this problem into two subproblems by setting (x + 0.5) equal to 0.415428267 and -0.415428267.Subproblem 1
x + 0.5 = 0.415428267 Simplifying x + 0.5 = 0.415428267 Reorder the terms: 0.5 + x = 0.415428267 Solving 0.5 + x = 0.415428267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.415428267 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.415428267 + -0.5 x = 0.415428267 + -0.5 Combine like terms: 0.415428267 + -0.5 = -0.084571733 x = -0.084571733 Simplifying x = -0.084571733Subproblem 2
x + 0.5 = -0.415428267 Simplifying x + 0.5 = -0.415428267 Reorder the terms: 0.5 + x = -0.415428267 Solving 0.5 + x = -0.415428267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.415428267 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.415428267 + -0.5 x = -0.415428267 + -0.5 Combine like terms: -0.415428267 + -0.5 = -0.915428267 x = -0.915428267 Simplifying x = -0.915428267Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.084571733, -0.915428267}
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