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Simplifying 12x2 + -42x + 6 = 26 Reorder the terms: 6 + -42x + 12x2 = 26 Solving 6 + -42x + 12x2 = 26 Solving for variable 'x'. Reorder the terms: 6 + -26 + -42x + 12x2 = 26 + -26 Combine like terms: 6 + -26 = -20 -20 + -42x + 12x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -20 + -42x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -21x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -21x + 6x2)' equal to zero and attempt to solve: Simplifying -10 + -21x + 6x2 = 0 Solving -10 + -21x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.666666667 + -3.5x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -3.5x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -3.5x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -3.5x + x2 = 0 + 1.666666667 -3.5x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -3.5x + x2 = 1.666666667 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 1.666666667 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 1.666666667 + 3.0625 Combine like terms: 1.666666667 + 3.0625 = 4.729166667 3.0625 + -3.5x + x2 = 4.729166667 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 4.729166667 Calculate the square root of the right side: 2.174664725 Break this problem into two subproblems by setting (x + -1.75) equal to 2.174664725 and -2.174664725.Subproblem 1
x + -1.75 = 2.174664725 Simplifying x + -1.75 = 2.174664725 Reorder the terms: -1.75 + x = 2.174664725 Solving -1.75 + x = 2.174664725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.174664725 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.174664725 + 1.75 x = 2.174664725 + 1.75 Combine like terms: 2.174664725 + 1.75 = 3.924664725 x = 3.924664725 Simplifying x = 3.924664725Subproblem 2
x + -1.75 = -2.174664725 Simplifying x + -1.75 = -2.174664725 Reorder the terms: -1.75 + x = -2.174664725 Solving -1.75 + x = -2.174664725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.174664725 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.174664725 + 1.75 x = -2.174664725 + 1.75 Combine like terms: -2.174664725 + 1.75 = -0.424664725 x = -0.424664725 Simplifying x = -0.424664725Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.924664725, -0.424664725}Solution
x = {3.924664725, -0.424664725}
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