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Simplifying 5x2 + 7x + 20 = 7x2 + 3 + -10 Reorder the terms: 20 + 7x + 5x2 = 7x2 + 3 + -10 Reorder the terms: 20 + 7x + 5x2 = 3 + -10 + 7x2 Combine like terms: 3 + -10 = -7 20 + 7x + 5x2 = -7 + 7x2 Solving 20 + 7x + 5x2 = -7 + 7x2 Solving for variable 'x'. Reorder the terms: 20 + 7 + 7x + 5x2 + -7x2 = -7 + 7x2 + 7 + -7x2 Combine like terms: 20 + 7 = 27 27 + 7x + 5x2 + -7x2 = -7 + 7x2 + 7 + -7x2 Combine like terms: 5x2 + -7x2 = -2x2 27 + 7x + -2x2 = -7 + 7x2 + 7 + -7x2 Reorder the terms: 27 + 7x + -2x2 = -7 + 7 + 7x2 + -7x2 Combine like terms: -7 + 7 = 0 27 + 7x + -2x2 = 0 + 7x2 + -7x2 27 + 7x + -2x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 27 + 7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -13.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '13.5' to each side of the equation. -13.5 + -3.5x + 13.5 + x2 = 0 + 13.5 Reorder the terms: -13.5 + 13.5 + -3.5x + x2 = 0 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + -3.5x + x2 = 0 + 13.5 -3.5x + x2 = 0 + 13.5 Combine like terms: 0 + 13.5 = 13.5 -3.5x + x2 = 13.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 13.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 13.5 + 3.0625 Combine like terms: 13.5 + 3.0625 = 16.5625 3.0625 + -3.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + -1.75) equal to 4.069705149 and -4.069705149.Subproblem 1
x + -1.75 = 4.069705149 Simplifying x + -1.75 = 4.069705149 Reorder the terms: -1.75 + x = 4.069705149 Solving -1.75 + x = 4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 4.069705149 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 4.069705149 + 1.75 x = 4.069705149 + 1.75 Combine like terms: 4.069705149 + 1.75 = 5.819705149 x = 5.819705149 Simplifying x = 5.819705149Subproblem 2
x + -1.75 = -4.069705149 Simplifying x + -1.75 = -4.069705149 Reorder the terms: -1.75 + x = -4.069705149 Solving -1.75 + x = -4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -4.069705149 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -4.069705149 + 1.75 x = -4.069705149 + 1.75 Combine like terms: -4.069705149 + 1.75 = -2.319705149 x = -2.319705149 Simplifying x = -2.319705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.819705149, -2.319705149}
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