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Simplifying 4x2 + 20x + -415 = 0 Reorder the terms: -415 + 20x + 4x2 = 0 Solving -415 + 20x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -103.75 + 5x + x2 = 0 Move the constant term to the right: Add '103.75' to each side of the equation. -103.75 + 5x + 103.75 + x2 = 0 + 103.75 Reorder the terms: -103.75 + 103.75 + 5x + x2 = 0 + 103.75 Combine like terms: -103.75 + 103.75 = 0.00 0.00 + 5x + x2 = 0 + 103.75 5x + x2 = 0 + 103.75 Combine like terms: 0 + 103.75 = 103.75 5x + x2 = 103.75 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 103.75 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 103.75 + 6.25 Combine like terms: 103.75 + 6.25 = 110 6.25 + 5x + x2 = 110 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (x + 2.5) equal to 10.488088482 and -10.488088482.Subproblem 1
x + 2.5 = 10.488088482 Simplifying x + 2.5 = 10.488088482 Reorder the terms: 2.5 + x = 10.488088482 Solving 2.5 + x = 10.488088482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.488088482 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.488088482 + -2.5 x = 10.488088482 + -2.5 Combine like terms: 10.488088482 + -2.5 = 7.988088482 x = 7.988088482 Simplifying x = 7.988088482Subproblem 2
x + 2.5 = -10.488088482 Simplifying x + 2.5 = -10.488088482 Reorder the terms: 2.5 + x = -10.488088482 Solving 2.5 + x = -10.488088482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.488088482 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.488088482 + -2.5 x = -10.488088482 + -2.5 Combine like terms: -10.488088482 + -2.5 = -12.988088482 x = -12.988088482 Simplifying x = -12.988088482Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.988088482, -12.988088482}
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