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Simplifying x2 + -2x + -3x + 6 = 2x2 + -3x + 10x + 21 Reorder the terms: 6 + -2x + -3x + x2 = 2x2 + -3x + 10x + 21 Combine like terms: -2x + -3x = -5x 6 + -5x + x2 = 2x2 + -3x + 10x + 21 Reorder the terms: 6 + -5x + x2 = 21 + -3x + 10x + 2x2 Combine like terms: -3x + 10x = 7x 6 + -5x + x2 = 21 + 7x + 2x2 Solving 6 + -5x + x2 = 21 + 7x + 2x2 Solving for variable 'x'. Reorder the terms: 6 + -21 + -5x + -7x + x2 + -2x2 = 21 + 7x + 2x2 + -21 + -7x + -2x2 Combine like terms: 6 + -21 = -15 -15 + -5x + -7x + x2 + -2x2 = 21 + 7x + 2x2 + -21 + -7x + -2x2 Combine like terms: -5x + -7x = -12x -15 + -12x + x2 + -2x2 = 21 + 7x + 2x2 + -21 + -7x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -15 + -12x + -1x2 = 21 + 7x + 2x2 + -21 + -7x + -2x2 Reorder the terms: -15 + -12x + -1x2 = 21 + -21 + 7x + -7x + 2x2 + -2x2 Combine like terms: 21 + -21 = 0 -15 + -12x + -1x2 = 0 + 7x + -7x + 2x2 + -2x2 -15 + -12x + -1x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 -15 + -12x + -1x2 = 0 + 2x2 + -2x2 -15 + -12x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -15 + -12x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 12x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 12x + x2)' equal to zero and attempt to solve: Simplifying 15 + 12x + x2 = 0 Solving 15 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 12x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 12x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 12x + x2 = 0 + -15 12x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 12x + x2 = -15 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -15 + 36 Reorder the terms: 36 + 12x + x2 = -15 + 36 Combine like terms: -15 + 36 = 21 36 + 12x + x2 = 21 Factor a perfect square on the left side: (x + 6)(x + 6) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + 6) equal to 4.582575695 and -4.582575695.Subproblem 1
x + 6 = 4.582575695 Simplifying x + 6 = 4.582575695 Reorder the terms: 6 + x = 4.582575695 Solving 6 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 4.582575695 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4.582575695 + -6 x = 4.582575695 + -6 Combine like terms: 4.582575695 + -6 = -1.417424305 x = -1.417424305 Simplifying x = -1.417424305Subproblem 2
x + 6 = -4.582575695 Simplifying x + 6 = -4.582575695 Reorder the terms: 6 + x = -4.582575695 Solving 6 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -4.582575695 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4.582575695 + -6 x = -4.582575695 + -6 Combine like terms: -4.582575695 + -6 = -10.582575695 x = -10.582575695 Simplifying x = -10.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.417424305, -10.582575695}Solution
x = {-1.417424305, -10.582575695}
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