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Simplifying 3x2 + -23x = 5x2 + -3x + -12 Reorder the terms: -23x + 3x2 = 5x2 + -3x + -12 Reorder the terms: -23x + 3x2 = -12 + -3x + 5x2 Solving -23x + 3x2 = -12 + -3x + 5x2 Solving for variable 'x'. Reorder the terms: 12 + -23x + 3x + 3x2 + -5x2 = -12 + -3x + 5x2 + 12 + 3x + -5x2 Combine like terms: -23x + 3x = -20x 12 + -20x + 3x2 + -5x2 = -12 + -3x + 5x2 + 12 + 3x + -5x2 Combine like terms: 3x2 + -5x2 = -2x2 12 + -20x + -2x2 = -12 + -3x + 5x2 + 12 + 3x + -5x2 Reorder the terms: 12 + -20x + -2x2 = -12 + 12 + -3x + 3x + 5x2 + -5x2 Combine like terms: -12 + 12 = 0 12 + -20x + -2x2 = 0 + -3x + 3x + 5x2 + -5x2 12 + -20x + -2x2 = -3x + 3x + 5x2 + -5x2 Combine like terms: -3x + 3x = 0 12 + -20x + -2x2 = 0 + 5x2 + -5x2 12 + -20x + -2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 12 + -20x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -10x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -10x + -1x2)' equal to zero and attempt to solve: Simplifying 6 + -10x + -1x2 = 0 Solving 6 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + 10x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 10x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 10x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 10x + x2 = 0 + 6 10x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 10x + x2 = 6 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 6 + 25 Reorder the terms: 25 + 10x + x2 = 6 + 25 Combine like terms: 6 + 25 = 31 25 + 10x + x2 = 31 Factor a perfect square on the left side: (x + 5)(x + 5) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 5) equal to 5.567764363 and -5.567764363.Subproblem 1
x + 5 = 5.567764363 Simplifying x + 5 = 5.567764363 Reorder the terms: 5 + x = 5.567764363 Solving 5 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.567764363 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.567764363 + -5 x = 5.567764363 + -5 Combine like terms: 5.567764363 + -5 = 0.567764363 x = 0.567764363 Simplifying x = 0.567764363Subproblem 2
x + 5 = -5.567764363 Simplifying x + 5 = -5.567764363 Reorder the terms: 5 + x = -5.567764363 Solving 5 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.567764363 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.567764363 + -5 x = -5.567764363 + -5 Combine like terms: -5.567764363 + -5 = -10.567764363 x = -10.567764363 Simplifying x = -10.567764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.567764363, -10.567764363}Solution
x = {0.567764363, -10.567764363}
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