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Simplifying 3x2 + -6x + -90 = 0 Reorder the terms: -90 + -6x + 3x2 = 0 Solving -90 + -6x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-30 + -2x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-30 + -2x + x2)' equal to zero and attempt to solve: Simplifying -30 + -2x + x2 = 0 Solving -30 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -2x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -2x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -2x + x2 = 0 + 30 -2x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -2x + x2 = 30 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 = 30 + 1 Reorder the terms: 1 + -2x + x2 = 30 + 1 Combine like terms: 30 + 1 = 31 1 + -2x + x2 = 31 Factor a perfect square on the left side: (x + -1)(x + -1) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + -1) equal to 5.567764363 and -5.567764363.Subproblem 1
x + -1 = 5.567764363 Simplifying x + -1 = 5.567764363 Reorder the terms: -1 + x = 5.567764363 Solving -1 + x = 5.567764363 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 = 5.567764363 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.567764363 + 1 x = 5.567764363 + 1 Combine like terms: 5.567764363 + 1 = 6.567764363 x = 6.567764363 Simplifying x = 6.567764363Subproblem 2
x + -1 = -5.567764363 Simplifying x + -1 = -5.567764363 Reorder the terms: -1 + x = -5.567764363 Solving -1 + x = -5.567764363 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 = -5.567764363 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.567764363 + 1 x = -5.567764363 + 1 Combine like terms: -5.567764363 + 1 = -4.567764363 x = -4.567764363 Simplifying x = -4.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.567764363, -4.567764363}Solution
x = {6.567764363, -4.567764363}
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