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Simplifying 102 = 10x2 + -1x Reorder the terms: 102 = -1x + 10x2 Solving 102 = -1x + 10x2 Solving for variable 'x'. Reorder the terms: 102 + x + -10x2 = -1x + x + 10x2 + -10x2 Combine like terms: -1x + x = 0 102 + x + -10x2 = 0 + 10x2 + -10x2 102 + x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 102 + x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -10.2 + -0.1x + x2 = 0 Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + -0.1x + 10.2 + x2 = 0 + 10.2 Reorder the terms: -10.2 + 10.2 + -0.1x + x2 = 0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + -0.1x + x2 = 0 + 10.2 -0.1x + x2 = 0 + 10.2 Combine like terms: 0 + 10.2 = 10.2 -0.1x + x2 = 10.2 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. -0.1x + 0.25 + x2 = 10.2 + 0.25 Reorder the terms: 0.25 + -0.1x + x2 = 10.2 + 0.25 Combine like terms: 10.2 + 0.25 = 10.45 0.25 + -0.1x + x2 = 10.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 10.45 Calculate the square root of the right side: 3.232645975 Break this problem into two subproblems by setting (x + 0.5) equal to 3.232645975 and -3.232645975.Subproblem 1
x + 0.5 = 3.232645975 Simplifying x + 0.5 = 3.232645975 Reorder the terms: 0.5 + x = 3.232645975 Solving 0.5 + x = 3.232645975 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 = 3.232645975 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.232645975 + -0.5 x = 3.232645975 + -0.5 Combine like terms: 3.232645975 + -0.5 = 2.732645975 x = 2.732645975 Simplifying x = 2.732645975Subproblem 2
x + 0.5 = -3.232645975 Simplifying x + 0.5 = -3.232645975 Reorder the terms: 0.5 + x = -3.232645975 Solving 0.5 + x = -3.232645975 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 = -3.232645975 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.232645975 + -0.5 x = -3.232645975 + -0.5 Combine like terms: -3.232645975 + -0.5 = -3.732645975 x = -3.732645975 Simplifying x = -3.732645975Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.732645975, -3.732645975}
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