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Simplifying 0 = 2x2 + 19x + 25 Reorder the terms: 0 = 25 + 19x + 2x2 Solving 0 = 25 + 19x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -25 = -25 -25 + -19x + -2x2 = 25 + 19x + 2x2 + -25 + -19x + -2x2 Reorder the terms: -25 + -19x + -2x2 = 25 + -25 + 19x + -19x + 2x2 + -2x2 Combine like terms: 25 + -25 = 0 -25 + -19x + -2x2 = 0 + 19x + -19x + 2x2 + -2x2 -25 + -19x + -2x2 = 19x + -19x + 2x2 + -2x2 Combine like terms: 19x + -19x = 0 -25 + -19x + -2x2 = 0 + 2x2 + -2x2 -25 + -19x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -25 + -19x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + 19x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(25 + 19x + 2x2)' equal to zero and attempt to solve: Simplifying 25 + 19x + 2x2 = 0 Solving 25 + 19x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + 9.5x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 9.5x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 9.5x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 9.5x + x2 = 0 + -12.5 9.5x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 9.5x + x2 = -12.5 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = -12.5 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = -12.5 + 22.5625 Combine like terms: -12.5 + 22.5625 = 10.0625 22.5625 + 9.5x + x2 = 10.0625 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (x + 4.75) equal to 3.172144385 and -3.172144385.Subproblem 1
x + 4.75 = 3.172144385 Simplifying x + 4.75 = 3.172144385 Reorder the terms: 4.75 + x = 3.172144385 Solving 4.75 + x = 3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 3.172144385 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 3.172144385 + -4.75 x = 3.172144385 + -4.75 Combine like terms: 3.172144385 + -4.75 = -1.577855615 x = -1.577855615 Simplifying x = -1.577855615Subproblem 2
x + 4.75 = -3.172144385 Simplifying x + 4.75 = -3.172144385 Reorder the terms: 4.75 + x = -3.172144385 Solving 4.75 + x = -3.172144385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -3.172144385 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -3.172144385 + -4.75 x = -3.172144385 + -4.75 Combine like terms: -3.172144385 + -4.75 = -7.922144385 x = -7.922144385 Simplifying x = -7.922144385Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.577855615, -7.922144385}Solution
x = {-1.577855615, -7.922144385}
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