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Simplifying 152 + -1x2 + -1x = 0 Reorder the terms: 152 + -1x + -1x2 = 0 Solving 152 + -1x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -152 + x + x2 = 0 Move the constant term to the right: Add '152' to each side of the equation. -152 + x + 152 + x2 = 0 + 152 Reorder the terms: -152 + 152 + x + x2 = 0 + 152 Combine like terms: -152 + 152 = 0 0 + x + x2 = 0 + 152 x + x2 = 0 + 152 Combine like terms: 0 + 152 = 152 x + x2 = 152 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. + 0.25 + x2 = 152 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 152 + 0.25 Combine like terms: 152 + 0.25 = 152.25 1.25 + x2 = 152.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 152.25 Calculate the square root of the right side: 12.338962679 Break this problem into two subproblems by setting (x + 0.5) equal to 12.338962679 and -12.338962679.Subproblem 1
x + 0.5 = 12.338962679 Simplifying x + 0.5 = 12.338962679 Reorder the terms: 0.5 + x = 12.338962679 Solving 0.5 + x = 12.338962679 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 = 12.338962679 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.338962679 + -0.5 x = 12.338962679 + -0.5 Combine like terms: 12.338962679 + -0.5 = 11.838962679 x = 11.838962679 Simplifying x = 11.838962679Subproblem 2
x + 0.5 = -12.338962679 Simplifying x + 0.5 = -12.338962679 Reorder the terms: 0.5 + x = -12.338962679 Solving 0.5 + x = -12.338962679 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 = -12.338962679 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.338962679 + -0.5 x = -12.338962679 + -0.5 Combine like terms: -12.338962679 + -0.5 = -12.838962679 x = -12.838962679 Simplifying x = -12.838962679Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.838962679, -12.838962679}
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