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Simplifying -21x2 + -14x + 42 = 0 Reorder the terms: 42 + -14x + -21x2 = 0 Solving 42 + -14x + -21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(6 + -2x + -3x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(6 + -2x + -3x2)' equal to zero and attempt to solve: Simplifying 6 + -2x + -3x2 = 0 Solving 6 + -2x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.6666666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.6666666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.6666666667x + x2 = 0 + 2 0.6666666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.6666666667x + x2 = 2 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 2 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 2 + 0.1111111112 Combine like terms: 2 + 0.1111111112 = 2.1111111112 0.1111111112 + 0.6666666667x + x2 = 2.1111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 2.1111111112 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 1.452966315 and -1.452966315.Subproblem 1
x + 0.3333333334 = 1.452966315 Simplifying x + 0.3333333334 = 1.452966315 Reorder the terms: 0.3333333334 + x = 1.452966315 Solving 0.3333333334 + x = 1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 1.452966315 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 1.452966315 + -0.3333333334 x = 1.452966315 + -0.3333333334 Combine like terms: 1.452966315 + -0.3333333334 = 1.1196329816 x = 1.1196329816 Simplifying x = 1.1196329816Subproblem 2
x + 0.3333333334 = -1.452966315 Simplifying x + 0.3333333334 = -1.452966315 Reorder the terms: 0.3333333334 + x = -1.452966315 Solving 0.3333333334 + x = -1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -1.452966315 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -1.452966315 + -0.3333333334 x = -1.452966315 + -0.3333333334 Combine like terms: -1.452966315 + -0.3333333334 = -1.7862996484 x = -1.7862996484 Simplifying x = -1.7862996484Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1196329816, -1.7862996484}Solution
x = {1.1196329816, -1.7862996484}
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