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Simplifying -0.6x2 + 48x + -480 = 0 Reorder the terms: -480 + 48x + -0.6x2 = 0 Solving -480 + 48x + -0.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. 800 + -80x + x2 = 0 Move the constant term to the right: Add '-800' to each side of the equation. 800 + -80x + -800 + x2 = 0 + -800 Reorder the terms: 800 + -800 + -80x + x2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + -80x + x2 = 0 + -800 -80x + x2 = 0 + -800 Combine like terms: 0 + -800 = -800 -80x + x2 = -800 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = -800 + 1600 Reorder the terms: 1600 + -80x + x2 = -800 + 1600 Combine like terms: -800 + 1600 = 800 1600 + -80x + x2 = 800 Factor a perfect square on the left side: (x + -40)(x + -40) = 800 Calculate the square root of the right side: 28.284271247 Break this problem into two subproblems by setting (x + -40) equal to 28.284271247 and -28.284271247.Subproblem 1
x + -40 = 28.284271247 Simplifying x + -40 = 28.284271247 Reorder the terms: -40 + x = 28.284271247 Solving -40 + x = 28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 28.284271247 + 40 Combine like terms: -40 + 40 = 0 0 + x = 28.284271247 + 40 x = 28.284271247 + 40 Combine like terms: 28.284271247 + 40 = 68.284271247 x = 68.284271247 Simplifying x = 68.284271247Subproblem 2
x + -40 = -28.284271247 Simplifying x + -40 = -28.284271247 Reorder the terms: -40 + x = -28.284271247 Solving -40 + x = -28.284271247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -28.284271247 + 40 Combine like terms: -40 + 40 = 0 0 + x = -28.284271247 + 40 x = -28.284271247 + 40 Combine like terms: -28.284271247 + 40 = 11.715728753 x = 11.715728753 Simplifying x = 11.715728753Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.284271247, 11.715728753}
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