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Simplifying -2x2 + -6x + 602 = 0 Reorder the terms: 602 + -6x + -2x2 = 0 Solving 602 + -6x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(301 + -3x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(301 + -3x + -1x2)' equal to zero and attempt to solve: Simplifying 301 + -3x + -1x2 = 0 Solving 301 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -301 + 3x + x2 = 0 Move the constant term to the right: Add '301' to each side of the equation. -301 + 3x + 301 + x2 = 0 + 301 Reorder the terms: -301 + 301 + 3x + x2 = 0 + 301 Combine like terms: -301 + 301 = 0 0 + 3x + x2 = 0 + 301 3x + x2 = 0 + 301 Combine like terms: 0 + 301 = 301 3x + x2 = 301 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 301 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 301 + 2.25 Combine like terms: 301 + 2.25 = 303.25 2.25 + 3x + x2 = 303.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 303.25 Calculate the square root of the right side: 17.414074767 Break this problem into two subproblems by setting (x + 1.5) equal to 17.414074767 and -17.414074767.Subproblem 1
x + 1.5 = 17.414074767 Simplifying x + 1.5 = 17.414074767 Reorder the terms: 1.5 + x = 17.414074767 Solving 1.5 + x = 17.414074767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 17.414074767 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 17.414074767 + -1.5 x = 17.414074767 + -1.5 Combine like terms: 17.414074767 + -1.5 = 15.914074767 x = 15.914074767 Simplifying x = 15.914074767Subproblem 2
x + 1.5 = -17.414074767 Simplifying x + 1.5 = -17.414074767 Reorder the terms: 1.5 + x = -17.414074767 Solving 1.5 + x = -17.414074767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -17.414074767 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -17.414074767 + -1.5 x = -17.414074767 + -1.5 Combine like terms: -17.414074767 + -1.5 = -18.914074767 x = -18.914074767 Simplifying x = -18.914074767Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.914074767, -18.914074767}Solution
x = {15.914074767, -18.914074767}
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