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Simplifying 5x * 5x + 3x + -18 = 0 Reorder the terms for easier multiplication: 5 * 5x * x + 3x + -18 = 0 Multiply 5 * 5 25x * x + 3x + -18 = 0 Multiply x * x 25x2 + 3x + -18 = 0 Reorder the terms: -18 + 3x + 25x2 = 0 Solving -18 + 3x + 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 + 0.12x + x2 = 0 Move the constant term to the right: Add '0.72' to each side of the equation. -0.72 + 0.12x + 0.72 + x2 = 0 + 0.72 Reorder the terms: -0.72 + 0.72 + 0.12x + x2 = 0 + 0.72 Combine like terms: -0.72 + 0.72 = 0.00 0.00 + 0.12x + x2 = 0 + 0.72 0.12x + x2 = 0 + 0.72 Combine like terms: 0 + 0.72 = 0.72 0.12x + x2 = 0.72 The x term is 0.12x. Take half its coefficient (0.06). Square it (0.0036) and add it to both sides. Add '0.0036' to each side of the equation. 0.12x + 0.0036 + x2 = 0.72 + 0.0036 Reorder the terms: 0.0036 + 0.12x + x2 = 0.72 + 0.0036 Combine like terms: 0.72 + 0.0036 = 0.7236 0.0036 + 0.12x + x2 = 0.7236 Factor a perfect square on the left side: (x + 0.06)(x + 0.06) = 0.7236 Calculate the square root of the right side: 0.850646813 Break this problem into two subproblems by setting (x + 0.06) equal to 0.850646813 and -0.850646813.Subproblem 1
x + 0.06 = 0.850646813 Simplifying x + 0.06 = 0.850646813 Reorder the terms: 0.06 + x = 0.850646813 Solving 0.06 + x = 0.850646813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = 0.850646813 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = 0.850646813 + -0.06 x = 0.850646813 + -0.06 Combine like terms: 0.850646813 + -0.06 = 0.790646813 x = 0.790646813 Simplifying x = 0.790646813Subproblem 2
x + 0.06 = -0.850646813 Simplifying x + 0.06 = -0.850646813 Reorder the terms: 0.06 + x = -0.850646813 Solving 0.06 + x = -0.850646813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = -0.850646813 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = -0.850646813 + -0.06 x = -0.850646813 + -0.06 Combine like terms: -0.850646813 + -0.06 = -0.910646813 x = -0.910646813 Simplifying x = -0.910646813Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.790646813, -0.910646813}
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