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Simplifying (52x + -5)(35 + x) = 7 Reorder the terms: (-5 + 52x)(35 + x) = 7 Multiply (-5 + 52x) * (35 + x) (-5(35 + x) + 52x * (35 + x)) = 7 ((35 * -5 + x * -5) + 52x * (35 + x)) = 7 ((-175 + -5x) + 52x * (35 + x)) = 7 (-175 + -5x + (35 * 52x + x * 52x)) = 7 (-175 + -5x + (1820x + 52x2)) = 7 Combine like terms: -5x + 1820x = 1815x (-175 + 1815x + 52x2) = 7 Solving -175 + 1815x + 52x2 = 7 Solving for variable 'x'. Reorder the terms: -175 + -7 + 1815x + 52x2 = 7 + -7 Combine like terms: -175 + -7 = -182 -182 + 1815x + 52x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -182 + 1815x + 52x2 = 0 Begin completing the square. Divide all terms by 52 the coefficient of the squared term: Divide each side by '52'. -3.5 + 34.90384615x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 34.90384615x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 34.90384615x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 34.90384615x + x2 = 0 + 3.5 34.90384615x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 34.90384615x + x2 = 3.5 The x term is 34.90384615x. Take half its coefficient (17.45192308). Square it (304.5696192) and add it to both sides. Add '304.5696192' to each side of the equation. 34.90384615x + 304.5696192 + x2 = 3.5 + 304.5696192 Reorder the terms: 304.5696192 + 34.90384615x + x2 = 3.5 + 304.5696192 Combine like terms: 3.5 + 304.5696192 = 308.0696192 304.5696192 + 34.90384615x + x2 = 308.0696192 Factor a perfect square on the left side: (x + 17.45192308)(x + 17.45192308) = 308.0696192 Calculate the square root of the right side: 17.551912124 Break this problem into two subproblems by setting (x + 17.45192308) equal to 17.551912124 and -17.551912124.Subproblem 1
x + 17.45192308 = 17.551912124 Simplifying x + 17.45192308 = 17.551912124 Reorder the terms: 17.45192308 + x = 17.551912124 Solving 17.45192308 + x = 17.551912124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.45192308' to each side of the equation. 17.45192308 + -17.45192308 + x = 17.551912124 + -17.45192308 Combine like terms: 17.45192308 + -17.45192308 = 0.00000000 0.00000000 + x = 17.551912124 + -17.45192308 x = 17.551912124 + -17.45192308 Combine like terms: 17.551912124 + -17.45192308 = 0.099989044 x = 0.099989044 Simplifying x = 0.099989044Subproblem 2
x + 17.45192308 = -17.551912124 Simplifying x + 17.45192308 = -17.551912124 Reorder the terms: 17.45192308 + x = -17.551912124 Solving 17.45192308 + x = -17.551912124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.45192308' to each side of the equation. 17.45192308 + -17.45192308 + x = -17.551912124 + -17.45192308 Combine like terms: 17.45192308 + -17.45192308 = 0.00000000 0.00000000 + x = -17.551912124 + -17.45192308 x = -17.551912124 + -17.45192308 Combine like terms: -17.551912124 + -17.45192308 = -35.003835204 x = -35.003835204 Simplifying x = -35.003835204Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.099989044, -35.003835204}
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