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Simplifying 2x2 + -6x = 155 Reorder the terms: -6x + 2x2 = 155 Solving -6x + 2x2 = 155 Solving for variable 'x'. Reorder the terms: -155 + -6x + 2x2 = 155 + -155 Combine like terms: 155 + -155 = 0 -155 + -6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -77.5 + -3x + x2 = 0 Move the constant term to the right: Add '77.5' to each side of the equation. -77.5 + -3x + 77.5 + x2 = 0 + 77.5 Reorder the terms: -77.5 + 77.5 + -3x + x2 = 0 + 77.5 Combine like terms: -77.5 + 77.5 = 0.0 0.0 + -3x + x2 = 0 + 77.5 -3x + x2 = 0 + 77.5 Combine like terms: 0 + 77.5 = 77.5 -3x + x2 = 77.5 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 77.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 77.5 + 2.25 Combine like terms: 77.5 + 2.25 = 79.75 2.25 + -3x + x2 = 79.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 79.75 Calculate the square root of the right side: 8.93028555 Break this problem into two subproblems by setting (x + -1.5) equal to 8.93028555 and -8.93028555.Subproblem 1
x + -1.5 = 8.93028555 Simplifying x + -1.5 = 8.93028555 Reorder the terms: -1.5 + x = 8.93028555 Solving -1.5 + x = 8.93028555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 8.93028555 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 8.93028555 + 1.5 x = 8.93028555 + 1.5 Combine like terms: 8.93028555 + 1.5 = 10.43028555 x = 10.43028555 Simplifying x = 10.43028555Subproblem 2
x + -1.5 = -8.93028555 Simplifying x + -1.5 = -8.93028555 Reorder the terms: -1.5 + x = -8.93028555 Solving -1.5 + x = -8.93028555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -8.93028555 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -8.93028555 + 1.5 x = -8.93028555 + 1.5 Combine like terms: -8.93028555 + 1.5 = -7.43028555 x = -7.43028555 Simplifying x = -7.43028555Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.43028555, -7.43028555}
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