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Simplifying 0 = 3x2 + -30x + 45 Reorder the terms: 0 = 45 + -30x + 3x2 Solving 0 = 45 + -30x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -45 = -45 -45 + 30x + -3x2 = 45 + -30x + 3x2 + -45 + 30x + -3x2 Reorder the terms: -45 + 30x + -3x2 = 45 + -45 + -30x + 30x + 3x2 + -3x2 Combine like terms: 45 + -45 = 0 -45 + 30x + -3x2 = 0 + -30x + 30x + 3x2 + -3x2 -45 + 30x + -3x2 = -30x + 30x + 3x2 + -3x2 Combine like terms: -30x + 30x = 0 -45 + 30x + -3x2 = 0 + 3x2 + -3x2 -45 + 30x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -45 + 30x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 10x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-15 + 10x + -1x2)' equal to zero and attempt to solve: Simplifying -15 + 10x + -1x2 = 0 Solving -15 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 15 + -10x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -10x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -10x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -10x + x2 = 0 + -15 -10x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -10x + x2 = -15 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -15 + 25 Reorder the terms: 25 + -10x + x2 = -15 + 25 Combine like terms: -15 + 25 = 10 25 + -10x + x2 = 10 Factor a perfect square on the left side: (x + -5)(x + -5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -5) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -5 = 3.16227766 Simplifying x + -5 = 3.16227766 Reorder the terms: -5 + x = 3.16227766 Solving -5 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.16227766 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.16227766 + 5 x = 3.16227766 + 5 Combine like terms: 3.16227766 + 5 = 8.16227766 x = 8.16227766 Simplifying x = 8.16227766Subproblem 2
x + -5 = -3.16227766 Simplifying x + -5 = -3.16227766 Reorder the terms: -5 + x = -3.16227766 Solving -5 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.16227766 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.16227766 + 5 x = -3.16227766 + 5 Combine like terms: -3.16227766 + 5 = 1.83772234 x = 1.83772234 Simplifying x = 1.83772234Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.16227766, 1.83772234}Solution
x = {8.16227766, 1.83772234}
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