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Simplifying 7x2 + 4x + -18 = 37 Reorder the terms: -18 + 4x + 7x2 = 37 Solving -18 + 4x + 7x2 = 37 Solving for variable 'x'. Reorder the terms: -18 + -37 + 4x + 7x2 = 37 + -37 Combine like terms: -18 + -37 = -55 -55 + 4x + 7x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -55 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -7.857142857 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '7.857142857' to each side of the equation. -7.857142857 + 0.5714285714x + 7.857142857 + x2 = 0 + 7.857142857 Reorder the terms: -7.857142857 + 7.857142857 + 0.5714285714x + x2 = 0 + 7.857142857 Combine like terms: -7.857142857 + 7.857142857 = 0.000000000 0.000000000 + 0.5714285714x + x2 = 0 + 7.857142857 0.5714285714x + x2 = 0 + 7.857142857 Combine like terms: 0 + 7.857142857 = 7.857142857 0.5714285714x + x2 = 7.857142857 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 7.857142857 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 7.857142857 + 0.08163265305 Combine like terms: 7.857142857 + 0.08163265305 = 7.93877551005 0.08163265305 + 0.5714285714x + x2 = 7.93877551005 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 7.93877551005 Calculate the square root of the right side: 2.817583275 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 2.817583275 and -2.817583275.Subproblem 1
x + 0.2857142857 = 2.817583275 Simplifying x + 0.2857142857 = 2.817583275 Reorder the terms: 0.2857142857 + x = 2.817583275 Solving 0.2857142857 + x = 2.817583275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 2.817583275 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 2.817583275 + -0.2857142857 x = 2.817583275 + -0.2857142857 Combine like terms: 2.817583275 + -0.2857142857 = 2.5318689893 x = 2.5318689893 Simplifying x = 2.5318689893Subproblem 2
x + 0.2857142857 = -2.817583275 Simplifying x + 0.2857142857 = -2.817583275 Reorder the terms: 0.2857142857 + x = -2.817583275 Solving 0.2857142857 + x = -2.817583275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -2.817583275 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -2.817583275 + -0.2857142857 x = -2.817583275 + -0.2857142857 Combine like terms: -2.817583275 + -0.2857142857 = -3.1032975607 x = -3.1032975607 Simplifying x = -3.1032975607Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5318689893, -3.1032975607}
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