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Simplifying 5x2 + -7x = 18 Reorder the terms: -7x + 5x2 = 18 Solving -7x + 5x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + -7x + 5x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + -1.4x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -1.4x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -1.4x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -1.4x + x2 = 0 + 3.6 -1.4x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -1.4x + x2 = 3.6 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 3.6 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 3.6 + 0.49 Combine like terms: 3.6 + 0.49 = 4.09 0.49 + -1.4x + x2 = 4.09 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 4.09 Calculate the square root of the right side: 2.022374842 Break this problem into two subproblems by setting (x + -0.7) equal to 2.022374842 and -2.022374842.Subproblem 1
x + -0.7 = 2.022374842 Simplifying x + -0.7 = 2.022374842 Reorder the terms: -0.7 + x = 2.022374842 Solving -0.7 + x = 2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 2.022374842 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 2.022374842 + 0.7 x = 2.022374842 + 0.7 Combine like terms: 2.022374842 + 0.7 = 2.722374842 x = 2.722374842 Simplifying x = 2.722374842Subproblem 2
x + -0.7 = -2.022374842 Simplifying x + -0.7 = -2.022374842 Reorder the terms: -0.7 + x = -2.022374842 Solving -0.7 + x = -2.022374842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -2.022374842 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -2.022374842 + 0.7 x = -2.022374842 + 0.7 Combine like terms: -2.022374842 + 0.7 = -1.322374842 x = -1.322374842 Simplifying x = -1.322374842Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.722374842, -1.322374842}
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