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Simplifying -14x2 = 12x + -5 + 9x + 7x2 + 8 Reorder the terms: -14x2 = -5 + 8 + 12x + 9x + 7x2 Combine like terms: -5 + 8 = 3 -14x2 = 3 + 12x + 9x + 7x2 Combine like terms: 12x + 9x = 21x -14x2 = 3 + 21x + 7x2 Solving -14x2 = 3 + 21x + 7x2 Solving for variable 'x'. Reorder the terms: -3 + -21x + -14x2 + -7x2 = 3 + 21x + 7x2 + -3 + -21x + -7x2 Combine like terms: -14x2 + -7x2 = -21x2 -3 + -21x + -21x2 = 3 + 21x + 7x2 + -3 + -21x + -7x2 Reorder the terms: -3 + -21x + -21x2 = 3 + -3 + 21x + -21x + 7x2 + -7x2 Combine like terms: 3 + -3 = 0 -3 + -21x + -21x2 = 0 + 21x + -21x + 7x2 + -7x2 -3 + -21x + -21x2 = 21x + -21x + 7x2 + -7x2 Combine like terms: 21x + -21x = 0 -3 + -21x + -21x2 = 0 + 7x2 + -7x2 -3 + -21x + -21x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -3 + -21x + -21x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(1 + 7x + 7x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(1 + 7x + 7x2)' equal to zero and attempt to solve: Simplifying 1 + 7x + 7x2 = 0 Solving 1 + 7x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x + x2 = 0 + -0.1428571429 x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 x + x2 = -0.1428571429 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -0.1428571429 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.1428571429 + 0.25 Combine like terms: -0.1428571429 + 0.25 = 0.1071428571 1.25 + x2 = 0.1071428571 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.1071428571 Calculate the square root of the right side: 0.327326835 Break this problem into two subproblems by setting (x + 0.5) equal to 0.327326835 and -0.327326835.Subproblem 1
x + 0.5 = 0.327326835 Simplifying x + 0.5 = 0.327326835 Reorder the terms: 0.5 + x = 0.327326835 Solving 0.5 + x = 0.327326835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.327326835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.327326835 + -0.5 x = 0.327326835 + -0.5 Combine like terms: 0.327326835 + -0.5 = -0.172673165 x = -0.172673165 Simplifying x = -0.172673165Subproblem 2
x + 0.5 = -0.327326835 Simplifying x + 0.5 = -0.327326835 Reorder the terms: 0.5 + x = -0.327326835 Solving 0.5 + x = -0.327326835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.327326835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.327326835 + -0.5 x = -0.327326835 + -0.5 Combine like terms: -0.327326835 + -0.5 = -0.827326835 x = -0.827326835 Simplifying x = -0.827326835Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.172673165, -0.827326835}Solution
x = {-0.172673165, -0.827326835}
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