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Simplifying 7x2 + 3x + 88 = 180 Reorder the terms: 88 + 3x + 7x2 = 180 Solving 88 + 3x + 7x2 = 180 Solving for variable 'x'. Reorder the terms: 88 + -180 + 3x + 7x2 = 180 + -180 Combine like terms: 88 + -180 = -92 -92 + 3x + 7x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -92 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -13.14285714 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '13.14285714' to each side of the equation. -13.14285714 + 0.4285714286x + 13.14285714 + x2 = 0 + 13.14285714 Reorder the terms: -13.14285714 + 13.14285714 + 0.4285714286x + x2 = 0 + 13.14285714 Combine like terms: -13.14285714 + 13.14285714 = 0.00000000 0.00000000 + 0.4285714286x + x2 = 0 + 13.14285714 0.4285714286x + x2 = 0 + 13.14285714 Combine like terms: 0 + 13.14285714 = 13.14285714 0.4285714286x + x2 = 13.14285714 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = 13.14285714 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = 13.14285714 + 0.04591836735 Combine like terms: 13.14285714 + 0.04591836735 = 13.18877550735 0.04591836735 + 0.4285714286x + x2 = 13.18877550735 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = 13.18877550735 Calculate the square root of the right side: 3.631635376 Break this problem into two subproblems by setting (x + 0.2142857143) equal to 3.631635376 and -3.631635376.Subproblem 1
x + 0.2142857143 = 3.631635376 Simplifying x + 0.2142857143 = 3.631635376 Reorder the terms: 0.2142857143 + x = 3.631635376 Solving 0.2142857143 + x = 3.631635376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 3.631635376 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 3.631635376 + -0.2142857143 x = 3.631635376 + -0.2142857143 Combine like terms: 3.631635376 + -0.2142857143 = 3.4173496617 x = 3.4173496617 Simplifying x = 3.4173496617Subproblem 2
x + 0.2142857143 = -3.631635376 Simplifying x + 0.2142857143 = -3.631635376 Reorder the terms: 0.2142857143 + x = -3.631635376 Solving 0.2142857143 + x = -3.631635376 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -3.631635376 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -3.631635376 + -0.2142857143 x = -3.631635376 + -0.2142857143 Combine like terms: -3.631635376 + -0.2142857143 = -3.8459210903 x = -3.8459210903 Simplifying x = -3.8459210903Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4173496617, -3.8459210903}
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