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Simplifying 2.5x2 + 1.5x + -90 = 0 Reorder the terms: -90 + 1.5x + 2.5x2 = 0 Solving -90 + 1.5x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. -36 + 0.6x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 0.6x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 0.6x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 0.6x + x2 = 0 + 36 0.6x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 0.6x + x2 = 36 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 36 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 36 + 0.09 Combine like terms: 36 + 0.09 = 36.09 0.09 + 0.6x + x2 = 36.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 36.09 Calculate the square root of the right side: 6.007495318 Break this problem into two subproblems by setting (x + 0.3) equal to 6.007495318 and -6.007495318.Subproblem 1
x + 0.3 = 6.007495318 Simplifying x + 0.3 = 6.007495318 Reorder the terms: 0.3 + x = 6.007495318 Solving 0.3 + x = 6.007495318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 6.007495318 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 6.007495318 + -0.3 x = 6.007495318 + -0.3 Combine like terms: 6.007495318 + -0.3 = 5.707495318 x = 5.707495318 Simplifying x = 5.707495318Subproblem 2
x + 0.3 = -6.007495318 Simplifying x + 0.3 = -6.007495318 Reorder the terms: 0.3 + x = -6.007495318 Solving 0.3 + x = -6.007495318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -6.007495318 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -6.007495318 + -0.3 x = -6.007495318 + -0.3 Combine like terms: -6.007495318 + -0.3 = -6.307495318 x = -6.307495318 Simplifying x = -6.307495318Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.707495318, -6.307495318}
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