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Simplifying 70 = x + 2(x)(x + 2) Reorder the terms: 70 = x + 2x(2 + x) 70 = x + (2 * 2x + x * 2x) 70 = x + (4x + 2x2) Combine like terms: x + 4x = 5x 70 = 5x + 2x2 Solving 70 = 5x + 2x2 Solving for variable 'x'. Reorder the terms: 70 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2 Combine like terms: 5x + -5x = 0 70 + -5x + -2x2 = 0 + 2x2 + -2x2 70 + -5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 70 + -5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -35 + 2.5x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + 2.5x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 2.5x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 2.5x + x2 = 0 + 35 2.5x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 2.5x + x2 = 35 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 35 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 35 + 1.5625 Combine like terms: 35 + 1.5625 = 36.5625 1.5625 + 2.5x + x2 = 36.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting (x + 1.25) equal to 6.046693311 and -6.046693311.Subproblem 1
x + 1.25 = 6.046693311 Simplifying x + 1.25 = 6.046693311 Reorder the terms: 1.25 + x = 6.046693311 Solving 1.25 + x = 6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 6.046693311 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 6.046693311 + -1.25 x = 6.046693311 + -1.25 Combine like terms: 6.046693311 + -1.25 = 4.796693311 x = 4.796693311 Simplifying x = 4.796693311Subproblem 2
x + 1.25 = -6.046693311 Simplifying x + 1.25 = -6.046693311 Reorder the terms: 1.25 + x = -6.046693311 Solving 1.25 + x = -6.046693311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -6.046693311 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -6.046693311 + -1.25 x = -6.046693311 + -1.25 Combine like terms: -6.046693311 + -1.25 = -7.296693311 x = -7.296693311 Simplifying x = -7.296693311Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.796693311, -7.296693311}
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