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Simplifying 0 = -5x2 + 20x + 30 Reorder the terms: 0 = 30 + 20x + -5x2 Solving 0 = 30 + 20x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -30 = -30 -30 + -20x + 5x2 = 30 + 20x + -5x2 + -30 + -20x + 5x2 Reorder the terms: -30 + -20x + 5x2 = 30 + -30 + 20x + -20x + -5x2 + 5x2 Combine like terms: 30 + -30 = 0 -30 + -20x + 5x2 = 0 + 20x + -20x + -5x2 + 5x2 -30 + -20x + 5x2 = 20x + -20x + -5x2 + 5x2 Combine like terms: 20x + -20x = 0 -30 + -20x + 5x2 = 0 + -5x2 + 5x2 -30 + -20x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -30 + -20x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + -4x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + -4x + x2)' equal to zero and attempt to solve: Simplifying -6 + -4x + x2 = 0 Solving -6 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -4x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -4x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -4x + x2 = 0 + 6 -4x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -4x + x2 = 6 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 6 + 4 Reorder the terms: 4 + -4x + x2 = 6 + 4 Combine like terms: 6 + 4 = 10 4 + -4x + x2 = 10 Factor a perfect square on the left side: (x + -2)(x + -2) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -2) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -2 = 3.16227766 Simplifying x + -2 = 3.16227766 Reorder the terms: -2 + x = 3.16227766 Solving -2 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.16227766 + 2 x = 3.16227766 + 2 Combine like terms: 3.16227766 + 2 = 5.16227766 x = 5.16227766 Simplifying x = 5.16227766Subproblem 2
x + -2 = -3.16227766 Simplifying x + -2 = -3.16227766 Reorder the terms: -2 + x = -3.16227766 Solving -2 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.16227766 + 2 x = -3.16227766 + 2 Combine like terms: -3.16227766 + 2 = -1.16227766 x = -1.16227766 Simplifying x = -1.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.16227766, -1.16227766}Solution
x = {5.16227766, -1.16227766}
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