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Simplifying 235 = 2.5x2 + 20x Reorder the terms: 235 = 20x + 2.5x2 Solving 235 = 20x + 2.5x2 Solving for variable 'x'. Reorder the terms: 235 + -20x + -2.5x2 = 20x + -20x + 2.5x2 + -2.5x2 Combine like terms: 20x + -20x = 0 235 + -20x + -2.5x2 = 0 + 2.5x2 + -2.5x2 235 + -20x + -2.5x2 = 2.5x2 + -2.5x2 Combine like terms: 2.5x2 + -2.5x2 = 0.0 235 + -20x + -2.5x2 = 0.0 Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. -94 + 8x + x2 = 0 Move the constant term to the right: Add '94' to each side of the equation. -94 + 8x + 94 + x2 = 0 + 94 Reorder the terms: -94 + 94 + 8x + x2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + 8x + x2 = 0 + 94 8x + x2 = 0 + 94 Combine like terms: 0 + 94 = 94 8x + x2 = 94 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 94 + 16 Reorder the terms: 16 + 8x + x2 = 94 + 16 Combine like terms: 94 + 16 = 110 16 + 8x + x2 = 110 Factor a perfect square on the left side: (x + 4)(x + 4) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (x + 4) equal to 10.488088482 and -10.488088482.Subproblem 1
x + 4 = 10.488088482 Simplifying x + 4 = 10.488088482 Reorder the terms: 4 + x = 10.488088482 Solving 4 + x = 10.488088482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 10.488088482 + -4 Combine like terms: 4 + -4 = 0 0 + x = 10.488088482 + -4 x = 10.488088482 + -4 Combine like terms: 10.488088482 + -4 = 6.488088482 x = 6.488088482 Simplifying x = 6.488088482Subproblem 2
x + 4 = -10.488088482 Simplifying x + 4 = -10.488088482 Reorder the terms: 4 + x = -10.488088482 Solving 4 + x = -10.488088482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -10.488088482 + -4 Combine like terms: 4 + -4 = 0 0 + x = -10.488088482 + -4 x = -10.488088482 + -4 Combine like terms: -10.488088482 + -4 = -14.488088482 x = -14.488088482 Simplifying x = -14.488088482Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.488088482, -14.488088482}
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