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Simplifying 6x2 + -12x + -90 = -18 Reorder the terms: -90 + -12x + 6x2 = -18 Solving -90 + -12x + 6x2 = -18 Solving for variable 'x'. Reorder the terms: -90 + 18 + -12x + 6x2 = -18 + 18 Combine like terms: -90 + 18 = -72 -72 + -12x + 6x2 = -18 + 18 Combine like terms: -18 + 18 = 0 -72 + -12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-12 + -2x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-12 + -2x + x2)' equal to zero and attempt to solve: Simplifying -12 + -2x + x2 = 0 Solving -12 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -2x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -2x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -2x + x2 = 0 + 12 -2x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -2x + x2 = 12 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 12 + 1 Reorder the terms: 1 + -2x + x2 = 12 + 1 Combine like terms: 12 + 1 = 13 1 + -2x + x2 = 13 Factor a perfect square on the left side: (x + -1)(x + -1) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -1) equal to 3.605551275 and -3.605551275.Subproblem 1
x + -1 = 3.605551275 Simplifying x + -1 = 3.605551275 Reorder the terms: -1 + x = 3.605551275 Solving -1 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.605551275 + 1 x = 3.605551275 + 1 Combine like terms: 3.605551275 + 1 = 4.605551275 x = 4.605551275 Simplifying x = 4.605551275Subproblem 2
x + -1 = -3.605551275 Simplifying x + -1 = -3.605551275 Reorder the terms: -1 + x = -3.605551275 Solving -1 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.605551275 + 1 x = -3.605551275 + 1 Combine like terms: -3.605551275 + 1 = -2.605551275 x = -2.605551275 Simplifying x = -2.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.605551275, -2.605551275}Solution
x = {4.605551275, -2.605551275}
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