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Simplifying 0 = 4x2 + 62x + 28 Reorder the terms: 0 = 28 + 62x + 4x2 Solving 0 = 28 + 62x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -28 = -28 -28 + -62x + -4x2 = 28 + 62x + 4x2 + -28 + -62x + -4x2 Reorder the terms: -28 + -62x + -4x2 = 28 + -28 + 62x + -62x + 4x2 + -4x2 Combine like terms: 28 + -28 = 0 -28 + -62x + -4x2 = 0 + 62x + -62x + 4x2 + -4x2 -28 + -62x + -4x2 = 62x + -62x + 4x2 + -4x2 Combine like terms: 62x + -62x = 0 -28 + -62x + -4x2 = 0 + 4x2 + -4x2 -28 + -62x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -28 + -62x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(14 + 31x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(14 + 31x + 2x2)' equal to zero and attempt to solve: Simplifying 14 + 31x + 2x2 = 0 Solving 14 + 31x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7 + 15.5x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 15.5x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 15.5x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 15.5x + x2 = 0 + -7 15.5x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 15.5x + x2 = -7 The x term is 15.5x. Take half its coefficient (7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. 15.5x + 60.0625 + x2 = -7 + 60.0625 Reorder the terms: 60.0625 + 15.5x + x2 = -7 + 60.0625 Combine like terms: -7 + 60.0625 = 53.0625 60.0625 + 15.5x + x2 = 53.0625 Factor a perfect square on the left side: (x + 7.75)(x + 7.75) = 53.0625 Calculate the square root of the right side: 7.284401142 Break this problem into two subproblems by setting (x + 7.75) equal to 7.284401142 and -7.284401142.Subproblem 1
x + 7.75 = 7.284401142 Simplifying x + 7.75 = 7.284401142 Reorder the terms: 7.75 + x = 7.284401142 Solving 7.75 + x = 7.284401142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = 7.284401142 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = 7.284401142 + -7.75 x = 7.284401142 + -7.75 Combine like terms: 7.284401142 + -7.75 = -0.465598858 x = -0.465598858 Simplifying x = -0.465598858Subproblem 2
x + 7.75 = -7.284401142 Simplifying x + 7.75 = -7.284401142 Reorder the terms: 7.75 + x = -7.284401142 Solving 7.75 + x = -7.284401142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.75' to each side of the equation. 7.75 + -7.75 + x = -7.284401142 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = -7.284401142 + -7.75 x = -7.284401142 + -7.75 Combine like terms: -7.284401142 + -7.75 = -15.034401142 x = -15.034401142 Simplifying x = -15.034401142Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.465598858, -15.034401142}Solution
x = {-0.465598858, -15.034401142}
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