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Simplifying 5x2 + 20x + -18 = 18 Reorder the terms: -18 + 20x + 5x2 = 18 Solving -18 + 20x + 5x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + -18 + 20x + 5x2 = 18 + -18 Combine like terms: -18 + -18 = -36 -36 + 20x + 5x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -36 + 20x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + 4x + x2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 4x + 7.2 + x2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 4x + x2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 4x + x2 = 0 + 7.2 4x + x2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 4x + x2 = 7.2 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 7.2 + 4 Reorder the terms: 4 + 4x + x2 = 7.2 + 4 Combine like terms: 7.2 + 4 = 11.2 4 + 4x + x2 = 11.2 Factor a perfect square on the left side: (x + 2)(x + 2) = 11.2 Calculate the square root of the right side: 3.346640106 Break this problem into two subproblems by setting (x + 2) equal to 3.346640106 and -3.346640106.Subproblem 1
x + 2 = 3.346640106 Simplifying x + 2 = 3.346640106 Reorder the terms: 2 + x = 3.346640106 Solving 2 + x = 3.346640106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.346640106 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.346640106 + -2 x = 3.346640106 + -2 Combine like terms: 3.346640106 + -2 = 1.346640106 x = 1.346640106 Simplifying x = 1.346640106Subproblem 2
x + 2 = -3.346640106 Simplifying x + 2 = -3.346640106 Reorder the terms: 2 + x = -3.346640106 Solving 2 + x = -3.346640106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.346640106 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.346640106 + -2 x = -3.346640106 + -2 Combine like terms: -3.346640106 + -2 = -5.346640106 x = -5.346640106 Simplifying x = -5.346640106Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.346640106, -5.346640106}
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