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Simplifying 0.2x2 + -24 = -13x Reorder the terms: -24 + 0.2x2 = -13x Solving -24 + 0.2x2 = -13x Solving for variable 'x'. Reorder the terms: -24 + 13x + 0.2x2 = -13x + 13x Combine like terms: -13x + 13x = 0 -24 + 13x + 0.2x2 = 0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -120 + 65x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 65x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 65x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 65x + x2 = 0 + 120 65x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 65x + x2 = 120 The x term is 65x. Take half its coefficient (32.5). Square it (1056.25) and add it to both sides. Add '1056.25' to each side of the equation. 65x + 1056.25 + x2 = 120 + 1056.25 Reorder the terms: 1056.25 + 65x + x2 = 120 + 1056.25 Combine like terms: 120 + 1056.25 = 1176.25 1056.25 + 65x + x2 = 1176.25 Factor a perfect square on the left side: (x + 32.5)(x + 32.5) = 1176.25 Calculate the square root of the right side: 34.296501279 Break this problem into two subproblems by setting (x + 32.5) equal to 34.296501279 and -34.296501279.Subproblem 1
x + 32.5 = 34.296501279 Simplifying x + 32.5 = 34.296501279 Reorder the terms: 32.5 + x = 34.296501279 Solving 32.5 + x = 34.296501279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32.5' to each side of the equation. 32.5 + -32.5 + x = 34.296501279 + -32.5 Combine like terms: 32.5 + -32.5 = 0.0 0.0 + x = 34.296501279 + -32.5 x = 34.296501279 + -32.5 Combine like terms: 34.296501279 + -32.5 = 1.796501279 x = 1.796501279 Simplifying x = 1.796501279Subproblem 2
x + 32.5 = -34.296501279 Simplifying x + 32.5 = -34.296501279 Reorder the terms: 32.5 + x = -34.296501279 Solving 32.5 + x = -34.296501279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32.5' to each side of the equation. 32.5 + -32.5 + x = -34.296501279 + -32.5 Combine like terms: 32.5 + -32.5 = 0.0 0.0 + x = -34.296501279 + -32.5 x = -34.296501279 + -32.5 Combine like terms: -34.296501279 + -32.5 = -66.796501279 x = -66.796501279 Simplifying x = -66.796501279Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.796501279, -66.796501279}
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