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Simplifying 4x2 + 36x + -35 = 35 Reorder the terms: -35 + 36x + 4x2 = 35 Solving -35 + 36x + 4x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + -35 + 36x + 4x2 = 35 + -35 Combine like terms: -35 + -35 = -70 -70 + 36x + 4x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -70 + 36x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-35 + 18x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + 18x + 2x2)' equal to zero and attempt to solve: Simplifying -35 + 18x + 2x2 = 0 Solving -35 + 18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + 9x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 9x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 9x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 9x + x2 = 0 + 17.5 9x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 9x + x2 = 17.5 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 17.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 17.5 + 20.25 Combine like terms: 17.5 + 20.25 = 37.75 20.25 + 9x + x2 = 37.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 37.75 Calculate the square root of the right side: 6.144102864 Break this problem into two subproblems by setting (x + 4.5) equal to 6.144102864 and -6.144102864.Subproblem 1
x + 4.5 = 6.144102864 Simplifying x + 4.5 = 6.144102864 Reorder the terms: 4.5 + x = 6.144102864 Solving 4.5 + x = 6.144102864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 6.144102864 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 6.144102864 + -4.5 x = 6.144102864 + -4.5 Combine like terms: 6.144102864 + -4.5 = 1.644102864 x = 1.644102864 Simplifying x = 1.644102864Subproblem 2
x + 4.5 = -6.144102864 Simplifying x + 4.5 = -6.144102864 Reorder the terms: 4.5 + x = -6.144102864 Solving 4.5 + x = -6.144102864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -6.144102864 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -6.144102864 + -4.5 x = -6.144102864 + -4.5 Combine like terms: -6.144102864 + -4.5 = -10.644102864 x = -10.644102864 Simplifying x = -10.644102864Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.644102864, -10.644102864}Solution
x = {1.644102864, -10.644102864}
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