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Simplifying 3x(x + -5) = 7x2 + -164 Reorder the terms: 3x(-5 + x) = 7x2 + -164 (-5 * 3x + x * 3x) = 7x2 + -164 (-15x + 3x2) = 7x2 + -164 Reorder the terms: -15x + 3x2 = -164 + 7x2 Solving -15x + 3x2 = -164 + 7x2 Solving for variable 'x'. Reorder the terms: 164 + -15x + 3x2 + -7x2 = -164 + 7x2 + 164 + -7x2 Combine like terms: 3x2 + -7x2 = -4x2 164 + -15x + -4x2 = -164 + 7x2 + 164 + -7x2 Reorder the terms: 164 + -15x + -4x2 = -164 + 164 + 7x2 + -7x2 Combine like terms: -164 + 164 = 0 164 + -15x + -4x2 = 0 + 7x2 + -7x2 164 + -15x + -4x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 164 + -15x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -41 + 3.75x + x2 = 0 Move the constant term to the right: Add '41' to each side of the equation. -41 + 3.75x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + 3.75x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 3.75x + x2 = 0 + 41 3.75x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 3.75x + x2 = 41 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 41 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 41 + 3.515625 Combine like terms: 41 + 3.515625 = 44.515625 3.515625 + 3.75x + x2 = 44.515625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 44.515625 Calculate the square root of the right side: 6.672003073 Break this problem into two subproblems by setting (x + 1.875) equal to 6.672003073 and -6.672003073.Subproblem 1
x + 1.875 = 6.672003073 Simplifying x + 1.875 = 6.672003073 Reorder the terms: 1.875 + x = 6.672003073 Solving 1.875 + x = 6.672003073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 6.672003073 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 6.672003073 + -1.875 x = 6.672003073 + -1.875 Combine like terms: 6.672003073 + -1.875 = 4.797003073 x = 4.797003073 Simplifying x = 4.797003073Subproblem 2
x + 1.875 = -6.672003073 Simplifying x + 1.875 = -6.672003073 Reorder the terms: 1.875 + x = -6.672003073 Solving 1.875 + x = -6.672003073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -6.672003073 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -6.672003073 + -1.875 x = -6.672003073 + -1.875 Combine like terms: -6.672003073 + -1.875 = -8.547003073 x = -8.547003073 Simplifying x = -8.547003073Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.797003073, -8.547003073}
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