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Simplifying 5x2 + -36x + 30 = 0 Reorder the terms: 30 + -36x + 5x2 = 0 Solving 30 + -36x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6 + -7.2x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -7.2x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -7.2x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7.2x + x2 = 0 + -6 -7.2x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -7.2x + x2 = -6 The x term is -7.2x. Take half its coefficient (-3.6). Square it (12.96) and add it to both sides. Add '12.96' to each side of the equation. -7.2x + 12.96 + x2 = -6 + 12.96 Reorder the terms: 12.96 + -7.2x + x2 = -6 + 12.96 Combine like terms: -6 + 12.96 = 6.96 12.96 + -7.2x + x2 = 6.96 Factor a perfect square on the left side: (x + -3.6)(x + -3.6) = 6.96 Calculate the square root of the right side: 2.638181192 Break this problem into two subproblems by setting (x + -3.6) equal to 2.638181192 and -2.638181192.Subproblem 1
x + -3.6 = 2.638181192 Simplifying x + -3.6 = 2.638181192 Reorder the terms: -3.6 + x = 2.638181192 Solving -3.6 + x = 2.638181192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = 2.638181192 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = 2.638181192 + 3.6 x = 2.638181192 + 3.6 Combine like terms: 2.638181192 + 3.6 = 6.238181192 x = 6.238181192 Simplifying x = 6.238181192Subproblem 2
x + -3.6 = -2.638181192 Simplifying x + -3.6 = -2.638181192 Reorder the terms: -3.6 + x = -2.638181192 Solving -3.6 + x = -2.638181192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.6' to each side of the equation. -3.6 + 3.6 + x = -2.638181192 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + x = -2.638181192 + 3.6 x = -2.638181192 + 3.6 Combine like terms: -2.638181192 + 3.6 = 0.961818808 x = 0.961818808 Simplifying x = 0.961818808Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.238181192, 0.961818808}
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