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Simplifying 28 = 4x2 + 34x Reorder the terms: 28 = 34x + 4x2 Solving 28 = 34x + 4x2 Solving for variable 'x'. Reorder the terms: 28 + -34x + -4x2 = 34x + -34x + 4x2 + -4x2 Combine like terms: 34x + -34x = 0 28 + -34x + -4x2 = 0 + 4x2 + -4x2 28 + -34x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 28 + -34x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -17x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + -17x + -2x2)' equal to zero and attempt to solve: Simplifying 14 + -17x + -2x2 = 0 Solving 14 + -17x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7 + 8.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 8.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 8.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 8.5x + x2 = 0 + 7 8.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 8.5x + x2 = 7 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 = 7 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 7 + 18.0625 Combine like terms: 7 + 18.0625 = 25.0625 18.0625 + 8.5x + x2 = 25.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 25.0625 Calculate the square root of the right side: 5.006246099 Break this problem into two subproblems by setting (x + 4.25) equal to 5.006246099 and -5.006246099.Subproblem 1
x + 4.25 = 5.006246099 Simplifying x + 4.25 = 5.006246099 Reorder the terms: 4.25 + x = 5.006246099 Solving 4.25 + x = 5.006246099 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 = 5.006246099 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 5.006246099 + -4.25 x = 5.006246099 + -4.25 Combine like terms: 5.006246099 + -4.25 = 0.756246099 x = 0.756246099 Simplifying x = 0.756246099Subproblem 2
x + 4.25 = -5.006246099 Simplifying x + 4.25 = -5.006246099 Reorder the terms: 4.25 + x = -5.006246099 Solving 4.25 + x = -5.006246099 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 = -5.006246099 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -5.006246099 + -4.25 x = -5.006246099 + -4.25 Combine like terms: -5.006246099 + -4.25 = -9.256246099 x = -9.256246099 Simplifying x = -9.256246099Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.756246099, -9.256246099}Solution
x = {0.756246099, -9.256246099}
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