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Simplifying 2x2 + 14x = 155 Reorder the terms: 14x + 2x2 = 155 Solving 14x + 2x2 = 155 Solving for variable 'x'. Reorder the terms: -155 + 14x + 2x2 = 155 + -155 Combine like terms: 155 + -155 = 0 -155 + 14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -77.5 + 7x + x2 = 0 Move the constant term to the right: Add '77.5' to each side of the equation. -77.5 + 7x + 77.5 + x2 = 0 + 77.5 Reorder the terms: -77.5 + 77.5 + 7x + x2 = 0 + 77.5 Combine like terms: -77.5 + 77.5 = 0.0 0.0 + 7x + x2 = 0 + 77.5 7x + x2 = 0 + 77.5 Combine like terms: 0 + 77.5 = 77.5 7x + x2 = 77.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 77.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 77.5 + 12.25 Combine like terms: 77.5 + 12.25 = 89.75 12.25 + 7x + x2 = 89.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 89.75 Calculate the square root of the right side: 9.473647661 Break this problem into two subproblems by setting (x + 3.5) equal to 9.473647661 and -9.473647661.Subproblem 1
x + 3.5 = 9.473647661 Simplifying x + 3.5 = 9.473647661 Reorder the terms: 3.5 + x = 9.473647661 Solving 3.5 + x = 9.473647661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 9.473647661 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.473647661 + -3.5 x = 9.473647661 + -3.5 Combine like terms: 9.473647661 + -3.5 = 5.973647661 x = 5.973647661 Simplifying x = 5.973647661Subproblem 2
x + 3.5 = -9.473647661 Simplifying x + 3.5 = -9.473647661 Reorder the terms: 3.5 + x = -9.473647661 Solving 3.5 + x = -9.473647661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -9.473647661 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.473647661 + -3.5 x = -9.473647661 + -3.5 Combine like terms: -9.473647661 + -3.5 = -12.973647661 x = -12.973647661 Simplifying x = -12.973647661Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.973647661, -12.973647661}
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