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Simplifying (2x)(2x) + 18x + 15 = 0 Remove parenthesis around (2x) 2x(2x) + 18x + 15 = 0 Remove parenthesis around (2x) 2x * 2x + 18x + 15 = 0 Reorder the terms for easier multiplication: 2 * 2x * x + 18x + 15 = 0 Multiply 2 * 2 4x * x + 18x + 15 = 0 Multiply x * x 4x2 + 18x + 15 = 0 Reorder the terms: 15 + 18x + 4x2 = 0 Solving 15 + 18x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + 4.5x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 4.5x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 4.5x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 4.5x + x2 = 0 + -3.75 4.5x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 4.5x + x2 = -3.75 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 = -3.75 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -3.75 + 5.0625 Combine like terms: -3.75 + 5.0625 = 1.3125 5.0625 + 4.5x + x2 = 1.3125 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (x + 2.25) equal to 1.145643924 and -1.145643924.Subproblem 1
x + 2.25 = 1.145643924 Simplifying x + 2.25 = 1.145643924 Reorder the terms: 2.25 + x = 1.145643924 Solving 2.25 + x = 1.145643924 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 = 1.145643924 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 1.145643924 + -2.25 x = 1.145643924 + -2.25 Combine like terms: 1.145643924 + -2.25 = -1.104356076 x = -1.104356076 Simplifying x = -1.104356076Subproblem 2
x + 2.25 = -1.145643924 Simplifying x + 2.25 = -1.145643924 Reorder the terms: 2.25 + x = -1.145643924 Solving 2.25 + x = -1.145643924 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 = -1.145643924 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -1.145643924 + -2.25 x = -1.145643924 + -2.25 Combine like terms: -1.145643924 + -2.25 = -3.395643924 x = -3.395643924 Simplifying x = -3.395643924Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.104356076, -3.395643924}
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