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Simplifying 0.1x2 + -15x + -100 = 0 Reorder the terms: -100 + -15x + 0.1x2 = 0 Solving -100 + -15x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -1000 + -150x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -150x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -150x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -150x + x2 = 0 + 1000 -150x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -150x + x2 = 1000 The x term is -150x. Take half its coefficient (-75). Square it (5625) and add it to both sides. Add '5625' to each side of the equation. -150x + 5625 + x2 = 1000 + 5625 Reorder the terms: 5625 + -150x + x2 = 1000 + 5625 Combine like terms: 1000 + 5625 = 6625 5625 + -150x + x2 = 6625 Factor a perfect square on the left side: (x + -75)(x + -75) = 6625 Calculate the square root of the right side: 81.39410298 Break this problem into two subproblems by setting (x + -75) equal to 81.39410298 and -81.39410298.Subproblem 1
x + -75 = 81.39410298 Simplifying x + -75 = 81.39410298 Reorder the terms: -75 + x = 81.39410298 Solving -75 + x = 81.39410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = 81.39410298 + 75 Combine like terms: -75 + 75 = 0 0 + x = 81.39410298 + 75 x = 81.39410298 + 75 Combine like terms: 81.39410298 + 75 = 156.39410298 x = 156.39410298 Simplifying x = 156.39410298Subproblem 2
x + -75 = -81.39410298 Simplifying x + -75 = -81.39410298 Reorder the terms: -75 + x = -81.39410298 Solving -75 + x = -81.39410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '75' to each side of the equation. -75 + 75 + x = -81.39410298 + 75 Combine like terms: -75 + 75 = 0 0 + x = -81.39410298 + 75 x = -81.39410298 + 75 Combine like terms: -81.39410298 + 75 = -6.39410298 x = -6.39410298 Simplifying x = -6.39410298Solution
The solution to the problem is based on the solutions from the subproblems. x = {156.39410298, -6.39410298}
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