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Simplifying 4x2 + 13x + 21x = 180 Reorder the terms: 13x + 21x + 4x2 = 180 Combine like terms: 13x + 21x = 34x 34x + 4x2 = 180 Solving 34x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 34x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 34x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 17x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + 17x + 2x2)' equal to zero and attempt to solve: Simplifying -90 + 17x + 2x2 = 0 Solving -90 + 17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -45 + 8.5x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 8.5x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 8.5x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 8.5x + x2 = 0 + 45 8.5x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 8.5x + x2 = 45 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 45 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 45 + 18.0625 Combine like terms: 45 + 18.0625 = 63.0625 18.0625 + 8.5x + x2 = 63.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 63.0625 Calculate the square root of the right side: 7.941190087 Break this problem into two subproblems by setting (x + 4.25) equal to 7.941190087 and -7.941190087.Subproblem 1
x + 4.25 = 7.941190087 Simplifying x + 4.25 = 7.941190087 Reorder the terms: 4.25 + x = 7.941190087 Solving 4.25 + x = 7.941190087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 7.941190087 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 7.941190087 + -4.25 x = 7.941190087 + -4.25 Combine like terms: 7.941190087 + -4.25 = 3.691190087 x = 3.691190087 Simplifying x = 3.691190087Subproblem 2
x + 4.25 = -7.941190087 Simplifying x + 4.25 = -7.941190087 Reorder the terms: 4.25 + x = -7.941190087 Solving 4.25 + x = -7.941190087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -7.941190087 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -7.941190087 + -4.25 x = -7.941190087 + -4.25 Combine like terms: -7.941190087 + -4.25 = -12.191190087 x = -12.191190087 Simplifying x = -12.191190087Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.691190087, -12.191190087}Solution
x = {3.691190087, -12.191190087}
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