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Simplifying -0.0075x2 + 0.5x + 5 = 0 Reorder the terms: 5 + 0.5x + -0.0075x2 = 0 Solving 5 + 0.5x + -0.0075x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0075 the coefficient of the squared term: Divide each side by '-0.0075'. -666.6666667 + -66.66666667x + x2 = 0 Move the constant term to the right: Add '666.6666667' to each side of the equation. -666.6666667 + -66.66666667x + 666.6666667 + x2 = 0 + 666.6666667 Reorder the terms: -666.6666667 + 666.6666667 + -66.66666667x + x2 = 0 + 666.6666667 Combine like terms: -666.6666667 + 666.6666667 = 0.0000000 0.0000000 + -66.66666667x + x2 = 0 + 666.6666667 -66.66666667x + x2 = 0 + 666.6666667 Combine like terms: 0 + 666.6666667 = 666.6666667 -66.66666667x + x2 = 666.6666667 The x term is -66.66666667x. Take half its coefficient (-33.33333334). Square it (1111.111112) and add it to both sides. Add '1111.111112' to each side of the equation. -66.66666667x + 1111.111112 + x2 = 666.6666667 + 1111.111112 Reorder the terms: 1111.111112 + -66.66666667x + x2 = 666.6666667 + 1111.111112 Combine like terms: 666.6666667 + 1111.111112 = 1777.7777787 1111.111112 + -66.66666667x + x2 = 1777.7777787 Factor a perfect square on the left side: (x + -33.33333334)(x + -33.33333334) = 1777.7777787 Calculate the square root of the right side: 42.163702147 Break this problem into two subproblems by setting (x + -33.33333334) equal to 42.163702147 and -42.163702147.Subproblem 1
x + -33.33333334 = 42.163702147 Simplifying x + -33.33333334 = 42.163702147 Reorder the terms: -33.33333334 + x = 42.163702147 Solving -33.33333334 + x = 42.163702147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.33333334' to each side of the equation. -33.33333334 + 33.33333334 + x = 42.163702147 + 33.33333334 Combine like terms: -33.33333334 + 33.33333334 = 0.00000000 0.00000000 + x = 42.163702147 + 33.33333334 x = 42.163702147 + 33.33333334 Combine like terms: 42.163702147 + 33.33333334 = 75.497035487 x = 75.497035487 Simplifying x = 75.497035487Subproblem 2
x + -33.33333334 = -42.163702147 Simplifying x + -33.33333334 = -42.163702147 Reorder the terms: -33.33333334 + x = -42.163702147 Solving -33.33333334 + x = -42.163702147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.33333334' to each side of the equation. -33.33333334 + 33.33333334 + x = -42.163702147 + 33.33333334 Combine like terms: -33.33333334 + 33.33333334 = 0.00000000 0.00000000 + x = -42.163702147 + 33.33333334 x = -42.163702147 + 33.33333334 Combine like terms: -42.163702147 + 33.33333334 = -8.830368807 x = -8.830368807 Simplifying x = -8.830368807Solution
The solution to the problem is based on the solutions from the subproblems. x = {75.497035487, -8.830368807}
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