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Simplifying (5x)(5x) + x + -18 = 0 Remove parenthesis around (5x) 5x(5x) + x + -18 = 0 Remove parenthesis around (5x) 5x * 5x + x + -18 = 0 Reorder the terms for easier multiplication: 5 * 5x * x + x + -18 = 0 Multiply 5 * 5 25x * x + x + -18 = 0 Multiply x * x 25x2 + x + -18 = 0 Reorder the terms: -18 + x + 25x2 = 0 Solving -18 + x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.72 + 0.04x + x2 = 0 Move the constant term to the right: Add '0.72' to each side of the equation. -0.72 + 0.04x + 0.72 + x2 = 0 + 0.72 Reorder the terms: -0.72 + 0.72 + 0.04x + x2 = 0 + 0.72 Combine like terms: -0.72 + 0.72 = 0.00 0.00 + 0.04x + x2 = 0 + 0.72 0.04x + x2 = 0 + 0.72 Combine like terms: 0 + 0.72 = 0.72 0.04x + x2 = 0.72 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. 0.04x + 0.25 + x2 = 0.72 + 0.25 Reorder the terms: 0.25 + 0.04x + x2 = 0.72 + 0.25 Combine like terms: 0.72 + 0.25 = 0.97 0.25 + 0.04x + x2 = 0.97 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.97 Calculate the square root of the right side: 0.98488578 Break this problem into two subproblems by setting (x + 0.5) equal to 0.98488578 and -0.98488578.Subproblem 1
x + 0.5 = 0.98488578 Simplifying x + 0.5 = 0.98488578 Reorder the terms: 0.5 + x = 0.98488578 Solving 0.5 + x = 0.98488578 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 = 0.98488578 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.98488578 + -0.5 x = 0.98488578 + -0.5 Combine like terms: 0.98488578 + -0.5 = 0.48488578 x = 0.48488578 Simplifying x = 0.48488578Subproblem 2
x + 0.5 = -0.98488578 Simplifying x + 0.5 = -0.98488578 Reorder the terms: 0.5 + x = -0.98488578 Solving 0.5 + x = -0.98488578 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 = -0.98488578 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.98488578 + -0.5 x = -0.98488578 + -0.5 Combine like terms: -0.98488578 + -0.5 = -1.48488578 x = -1.48488578 Simplifying x = -1.48488578Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.48488578, -1.48488578}
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