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Simplifying 2x2 + 9 = 30x Reorder the terms: 9 + 2x2 = 30x Solving 9 + 2x2 = 30x Solving for variable 'x'. Reorder the terms: 9 + -30x + 2x2 = 30x + -30x Combine like terms: 30x + -30x = 0 9 + -30x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -15x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -15x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -15x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -15x + x2 = 0 + -4.5 -15x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -15x + x2 = -4.5 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -4.5 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -4.5 + 56.25 Combine like terms: -4.5 + 56.25 = 51.75 56.25 + -15x + x2 = 51.75 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 51.75 Calculate the square root of the right side: 7.193747285 Break this problem into two subproblems by setting (x + -7.5) equal to 7.193747285 and -7.193747285.Subproblem 1
x + -7.5 = 7.193747285 Simplifying x + -7.5 = 7.193747285 Reorder the terms: -7.5 + x = 7.193747285 Solving -7.5 + x = 7.193747285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.193747285 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.193747285 + 7.5 x = 7.193747285 + 7.5 Combine like terms: 7.193747285 + 7.5 = 14.693747285 x = 14.693747285 Simplifying x = 14.693747285Subproblem 2
x + -7.5 = -7.193747285 Simplifying x + -7.5 = -7.193747285 Reorder the terms: -7.5 + x = -7.193747285 Solving -7.5 + x = -7.193747285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.193747285 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.193747285 + 7.5 x = -7.193747285 + 7.5 Combine like terms: -7.193747285 + 7.5 = 0.306252715 x = 0.306252715 Simplifying x = 0.306252715Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.693747285, 0.306252715}
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