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Simplifying 0 = 0.5x2 + 10x + -351 Reorder the terms: 0 = -351 + 10x + 0.5x2 Solving 0 = -351 + 10x + 0.5x2 Solving for variable 'x'. Combine like terms: 0 + 351 = 351 351 + -10x + -0.5x2 = -351 + 10x + 0.5x2 + 351 + -10x + -0.5x2 Reorder the terms: 351 + -10x + -0.5x2 = -351 + 351 + 10x + -10x + 0.5x2 + -0.5x2 Combine like terms: -351 + 351 = 0 351 + -10x + -0.5x2 = 0 + 10x + -10x + 0.5x2 + -0.5x2 351 + -10x + -0.5x2 = 10x + -10x + 0.5x2 + -0.5x2 Combine like terms: 10x + -10x = 0 351 + -10x + -0.5x2 = 0 + 0.5x2 + -0.5x2 351 + -10x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 351 + -10x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -702 + 20x + x2 = 0 Move the constant term to the right: Add '702' to each side of the equation. -702 + 20x + 702 + x2 = 0 + 702 Reorder the terms: -702 + 702 + 20x + x2 = 0 + 702 Combine like terms: -702 + 702 = 0 0 + 20x + x2 = 0 + 702 20x + x2 = 0 + 702 Combine like terms: 0 + 702 = 702 20x + x2 = 702 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 702 + 100 Reorder the terms: 100 + 20x + x2 = 702 + 100 Combine like terms: 702 + 100 = 802 100 + 20x + x2 = 802 Factor a perfect square on the left side: (x + 10)(x + 10) = 802 Calculate the square root of the right side: 28.319604517 Break this problem into two subproblems by setting (x + 10) equal to 28.319604517 and -28.319604517.Subproblem 1
x + 10 = 28.319604517 Simplifying x + 10 = 28.319604517 Reorder the terms: 10 + x = 28.319604517 Solving 10 + x = 28.319604517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 28.319604517 + -10 Combine like terms: 10 + -10 = 0 0 + x = 28.319604517 + -10 x = 28.319604517 + -10 Combine like terms: 28.319604517 + -10 = 18.319604517 x = 18.319604517 Simplifying x = 18.319604517Subproblem 2
x + 10 = -28.319604517 Simplifying x + 10 = -28.319604517 Reorder the terms: 10 + x = -28.319604517 Solving 10 + x = -28.319604517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -28.319604517 + -10 Combine like terms: 10 + -10 = 0 0 + x = -28.319604517 + -10 x = -28.319604517 + -10 Combine like terms: -28.319604517 + -10 = -38.319604517 x = -38.319604517 Simplifying x = -38.319604517Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.319604517, -38.319604517}
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