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Simplifying 61(4x + 17) * 5x + 5 = 132 Reorder the terms: 61(17 + 4x) * 5x + 5 = 132 Reorder the terms for easier multiplication: 61 * 5x(17 + 4x) + 5 = 132 Multiply 61 * 5 305x(17 + 4x) + 5 = 132 (17 * 305x + 4x * 305x) + 5 = 132 (5185x + 1220x2) + 5 = 132 Reorder the terms: 5 + 5185x + 1220x2 = 132 Solving 5 + 5185x + 1220x2 = 132 Solving for variable 'x'. Reorder the terms: 5 + -132 + 5185x + 1220x2 = 132 + -132 Combine like terms: 5 + -132 = -127 -127 + 5185x + 1220x2 = 132 + -132 Combine like terms: 132 + -132 = 0 -127 + 5185x + 1220x2 = 0 Begin completing the square. Divide all terms by 1220 the coefficient of the squared term: Divide each side by '1220'. -0.1040983607 + 4.25x + x2 = 0.0 Move the constant term to the right: Add '0.1040983607' to each side of the equation. -0.1040983607 + 4.25x + 0.1040983607 + x2 = 0.0 + 0.1040983607 Reorder the terms: -0.1040983607 + 0.1040983607 + 4.25x + x2 = 0.0 + 0.1040983607 Combine like terms: -0.1040983607 + 0.1040983607 = 0.0000000000 0.0000000000 + 4.25x + x2 = 0.0 + 0.1040983607 4.25x + x2 = 0.0 + 0.1040983607 Combine like terms: 0.0 + 0.1040983607 = 0.1040983607 4.25x + x2 = 0.1040983607 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 0.1040983607 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 0.1040983607 + 4.515625 Combine like terms: 0.1040983607 + 4.515625 = 4.6197233607 4.515625 + 4.25x + x2 = 4.6197233607 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 4.6197233607 Calculate the square root of the right side: 2.149354173 Break this problem into two subproblems by setting (x + 2.125) equal to 2.149354173 and -2.149354173.Subproblem 1
x + 2.125 = 2.149354173 Simplifying x + 2.125 = 2.149354173 Reorder the terms: 2.125 + x = 2.149354173 Solving 2.125 + x = 2.149354173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 2.149354173 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 2.149354173 + -2.125 x = 2.149354173 + -2.125 Combine like terms: 2.149354173 + -2.125 = 0.024354173 x = 0.024354173 Simplifying x = 0.024354173Subproblem 2
x + 2.125 = -2.149354173 Simplifying x + 2.125 = -2.149354173 Reorder the terms: 2.125 + x = -2.149354173 Solving 2.125 + x = -2.149354173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -2.149354173 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -2.149354173 + -2.125 x = -2.149354173 + -2.125 Combine like terms: -2.149354173 + -2.125 = -4.274354173 x = -4.274354173 Simplifying x = -4.274354173Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.024354173, -4.274354173}
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