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Simplifying 12.5 = x2 + x Reorder the terms: 12.5 = x + x2 Solving 12.5 = x + x2 Solving for variable 'x'. Reorder the terms: 12.5 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 12.5 + -1x + -1x2 = 0 + x2 + -1x2 12.5 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12.5 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12.5 + x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x + x2 = 0 + 12.5 x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 x + x2 = 12.5 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 = 12.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 12.5 + 0.25 Combine like terms: 12.5 + 0.25 = 12.75 1.25 + x2 = 12.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (x + 0.5) equal to 3.570714214 and -3.570714214.Subproblem 1
x + 0.5 = 3.570714214 Simplifying x + 0.5 = 3.570714214 Reorder the terms: 0.5 + x = 3.570714214 Solving 0.5 + x = 3.570714214 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 = 3.570714214 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.570714214 + -0.5 x = 3.570714214 + -0.5 Combine like terms: 3.570714214 + -0.5 = 3.070714214 x = 3.070714214 Simplifying x = 3.070714214Subproblem 2
x + 0.5 = -3.570714214 Simplifying x + 0.5 = -3.570714214 Reorder the terms: 0.5 + x = -3.570714214 Solving 0.5 + x = -3.570714214 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 = -3.570714214 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.570714214 + -0.5 x = -3.570714214 + -0.5 Combine like terms: -3.570714214 + -0.5 = -4.070714214 x = -4.070714214 Simplifying x = -4.070714214Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.070714214, -4.070714214}
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