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Simplifying (92 + -7x)(103 + -4x) = 129 Multiply (92 + -7x) * (103 + -4x) (92(103 + -4x) + -7x * (103 + -4x)) = 129 ((103 * 92 + -4x * 92) + -7x * (103 + -4x)) = 129 ((9476 + -368x) + -7x * (103 + -4x)) = 129 (9476 + -368x + (103 * -7x + -4x * -7x)) = 129 (9476 + -368x + (-721x + 28x2)) = 129 Combine like terms: -368x + -721x = -1089x (9476 + -1089x + 28x2) = 129 Solving 9476 + -1089x + 28x2 = 129 Solving for variable 'x'. Reorder the terms: 9476 + -129 + -1089x + 28x2 = 129 + -129 Combine like terms: 9476 + -129 = 9347 9347 + -1089x + 28x2 = 129 + -129 Combine like terms: 129 + -129 = 0 9347 + -1089x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 333.8214286 + -38.89285714x + x2 = 0 Move the constant term to the right: Add '-333.8214286' to each side of the equation. 333.8214286 + -38.89285714x + -333.8214286 + x2 = 0 + -333.8214286 Reorder the terms: 333.8214286 + -333.8214286 + -38.89285714x + x2 = 0 + -333.8214286 Combine like terms: 333.8214286 + -333.8214286 = 0.0000000 0.0000000 + -38.89285714x + x2 = 0 + -333.8214286 -38.89285714x + x2 = 0 + -333.8214286 Combine like terms: 0 + -333.8214286 = -333.8214286 -38.89285714x + x2 = -333.8214286 The x term is -38.89285714x. Take half its coefficient (-19.44642857). Square it (378.1635841) and add it to both sides. Add '378.1635841' to each side of the equation. -38.89285714x + 378.1635841 + x2 = -333.8214286 + 378.1635841 Reorder the terms: 378.1635841 + -38.89285714x + x2 = -333.8214286 + 378.1635841 Combine like terms: -333.8214286 + 378.1635841 = 44.3421555 378.1635841 + -38.89285714x + x2 = 44.3421555 Factor a perfect square on the left side: (x + -19.44642857)(x + -19.44642857) = 44.3421555 Calculate the square root of the right side: 6.658990577 Break this problem into two subproblems by setting (x + -19.44642857) equal to 6.658990577 and -6.658990577.Subproblem 1
x + -19.44642857 = 6.658990577 Simplifying x + -19.44642857 = 6.658990577 Reorder the terms: -19.44642857 + x = 6.658990577 Solving -19.44642857 + x = 6.658990577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.44642857' to each side of the equation. -19.44642857 + 19.44642857 + x = 6.658990577 + 19.44642857 Combine like terms: -19.44642857 + 19.44642857 = 0.00000000 0.00000000 + x = 6.658990577 + 19.44642857 x = 6.658990577 + 19.44642857 Combine like terms: 6.658990577 + 19.44642857 = 26.105419147 x = 26.105419147 Simplifying x = 26.105419147Subproblem 2
x + -19.44642857 = -6.658990577 Simplifying x + -19.44642857 = -6.658990577 Reorder the terms: -19.44642857 + x = -6.658990577 Solving -19.44642857 + x = -6.658990577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.44642857' to each side of the equation. -19.44642857 + 19.44642857 + x = -6.658990577 + 19.44642857 Combine like terms: -19.44642857 + 19.44642857 = 0.00000000 0.00000000 + x = -6.658990577 + 19.44642857 x = -6.658990577 + 19.44642857 Combine like terms: -6.658990577 + 19.44642857 = 12.787437993 x = 12.787437993 Simplifying x = 12.787437993Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.105419147, 12.787437993}
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