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Simplifying 0 = 0.8x2 + -19x + 40 Reorder the terms: 0 = 40 + -19x + 0.8x2 Solving 0 = 40 + -19x + 0.8x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + 19x + -0.8x2 = 40 + -19x + 0.8x2 + -40 + 19x + -0.8x2 Reorder the terms: -40 + 19x + -0.8x2 = 40 + -40 + -19x + 19x + 0.8x2 + -0.8x2 Combine like terms: 40 + -40 = 0 -40 + 19x + -0.8x2 = 0 + -19x + 19x + 0.8x2 + -0.8x2 -40 + 19x + -0.8x2 = -19x + 19x + 0.8x2 + -0.8x2 Combine like terms: -19x + 19x = 0 -40 + 19x + -0.8x2 = 0 + 0.8x2 + -0.8x2 -40 + 19x + -0.8x2 = 0.8x2 + -0.8x2 Combine like terms: 0.8x2 + -0.8x2 = 0.0 -40 + 19x + -0.8x2 = 0.0 Begin completing the square. Divide all terms by -0.8 the coefficient of the squared term: Divide each side by '-0.8'. 50 + -23.75x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -23.75x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -23.75x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -23.75x + x2 = 0 + -50 -23.75x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -23.75x + x2 = -50 The x term is -23.75x. Take half its coefficient (-11.875). Square it (141.015625) and add it to both sides. Add '141.015625' to each side of the equation. -23.75x + 141.015625 + x2 = -50 + 141.015625 Reorder the terms: 141.015625 + -23.75x + x2 = -50 + 141.015625 Combine like terms: -50 + 141.015625 = 91.015625 141.015625 + -23.75x + x2 = 91.015625 Factor a perfect square on the left side: (x + -11.875)(x + -11.875) = 91.015625 Calculate the square root of the right side: 9.540210952 Break this problem into two subproblems by setting (x + -11.875) equal to 9.540210952 and -9.540210952.Subproblem 1
x + -11.875 = 9.540210952 Simplifying x + -11.875 = 9.540210952 Reorder the terms: -11.875 + x = 9.540210952 Solving -11.875 + x = 9.540210952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.875' to each side of the equation. -11.875 + 11.875 + x = 9.540210952 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + x = 9.540210952 + 11.875 x = 9.540210952 + 11.875 Combine like terms: 9.540210952 + 11.875 = 21.415210952 x = 21.415210952 Simplifying x = 21.415210952Subproblem 2
x + -11.875 = -9.540210952 Simplifying x + -11.875 = -9.540210952 Reorder the terms: -11.875 + x = -9.540210952 Solving -11.875 + x = -9.540210952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.875' to each side of the equation. -11.875 + 11.875 + x = -9.540210952 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + x = -9.540210952 + 11.875 x = -9.540210952 + 11.875 Combine like terms: -9.540210952 + 11.875 = 2.334789048 x = 2.334789048 Simplifying x = 2.334789048Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.415210952, 2.334789048}
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