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Simplifying -2x2 + -14x + 30 = 0 Reorder the terms: 30 + -14x + -2x2 = 0 Solving 30 + -14x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -7x + -1x2)' equal to zero and attempt to solve: Simplifying 15 + -7x + -1x2 = 0 Solving 15 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + 7x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 7x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 7x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 7x + x2 = 0 + 15 7x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 7x + x2 = 15 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 15 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 15 + 12.25 Combine like terms: 15 + 12.25 = 27.25 12.25 + 7x + x2 = 27.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + 3.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + 3.5 = 5.220153254 Simplifying x + 3.5 = 5.220153254 Reorder the terms: 3.5 + x = 5.220153254 Solving 3.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 5.220153254 + -3.5 x = 5.220153254 + -3.5 Combine like terms: 5.220153254 + -3.5 = 1.720153254 x = 1.720153254 Simplifying x = 1.720153254Subproblem 2
x + 3.5 = -5.220153254 Simplifying x + 3.5 = -5.220153254 Reorder the terms: 3.5 + x = -5.220153254 Solving 3.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -5.220153254 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -5.220153254 + -3.5 x = -5.220153254 + -3.5 Combine like terms: -5.220153254 + -3.5 = -8.720153254 x = -8.720153254 Simplifying x = -8.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.720153254, -8.720153254}Solution
x = {1.720153254, -8.720153254}
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