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Simplifying 4x2 + 18x + -100 = 0 Reorder the terms: -100 + 18x + 4x2 = 0 Solving -100 + 18x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 9x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying -50 + 9x + 2x2 = 0 Solving -50 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25 + 4.5x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 4.5x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 4.5x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 4.5x + x2 = 0 + 25 4.5x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 4.5x + x2 = 25 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 25 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 25 + 5.0625 Combine like terms: 25 + 5.0625 = 30.0625 5.0625 + 4.5x + x2 = 30.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 30.0625 Calculate the square root of the right side: 5.48292805 Break this problem into two subproblems by setting (x + 2.25) equal to 5.48292805 and -5.48292805.Subproblem 1
x + 2.25 = 5.48292805 Simplifying x + 2.25 = 5.48292805 Reorder the terms: 2.25 + x = 5.48292805 Solving 2.25 + x = 5.48292805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 5.48292805 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 5.48292805 + -2.25 x = 5.48292805 + -2.25 Combine like terms: 5.48292805 + -2.25 = 3.23292805 x = 3.23292805 Simplifying x = 3.23292805Subproblem 2
x + 2.25 = -5.48292805 Simplifying x + 2.25 = -5.48292805 Reorder the terms: 2.25 + x = -5.48292805 Solving 2.25 + x = -5.48292805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -5.48292805 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -5.48292805 + -2.25 x = -5.48292805 + -2.25 Combine like terms: -5.48292805 + -2.25 = -7.73292805 x = -7.73292805 Simplifying x = -7.73292805Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.23292805, -7.73292805}Solution
x = {3.23292805, -7.73292805}
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