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Simplifying 0 = -3x2 + 28x + 144 Reorder the terms: 0 = 144 + 28x + -3x2 Solving 0 = 144 + 28x + -3x2 Solving for variable 'x'. Combine like terms: 0 + -144 = -144 -144 + -28x + 3x2 = 144 + 28x + -3x2 + -144 + -28x + 3x2 Reorder the terms: -144 + -28x + 3x2 = 144 + -144 + 28x + -28x + -3x2 + 3x2 Combine like terms: 144 + -144 = 0 -144 + -28x + 3x2 = 0 + 28x + -28x + -3x2 + 3x2 -144 + -28x + 3x2 = 28x + -28x + -3x2 + 3x2 Combine like terms: 28x + -28x = 0 -144 + -28x + 3x2 = 0 + -3x2 + 3x2 -144 + -28x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 -144 + -28x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -48 + -9.333333333x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -9.333333333x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -9.333333333x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -9.333333333x + x2 = 0 + 48 -9.333333333x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -9.333333333x + x2 = 48 The x term is -9.333333333x. Take half its coefficient (-4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. -9.333333333x + 21.77777778 + x2 = 48 + 21.77777778 Reorder the terms: 21.77777778 + -9.333333333x + x2 = 48 + 21.77777778 Combine like terms: 48 + 21.77777778 = 69.77777778 21.77777778 + -9.333333333x + x2 = 69.77777778 Factor a perfect square on the left side: (x + -4.666666667)(x + -4.666666667) = 69.77777778 Calculate the square root of the right side: 8.353309391 Break this problem into two subproblems by setting (x + -4.666666667) equal to 8.353309391 and -8.353309391.Subproblem 1
x + -4.666666667 = 8.353309391 Simplifying x + -4.666666667 = 8.353309391 Reorder the terms: -4.666666667 + x = 8.353309391 Solving -4.666666667 + x = 8.353309391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = 8.353309391 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = 8.353309391 + 4.666666667 x = 8.353309391 + 4.666666667 Combine like terms: 8.353309391 + 4.666666667 = 13.019976058 x = 13.019976058 Simplifying x = 13.019976058Subproblem 2
x + -4.666666667 = -8.353309391 Simplifying x + -4.666666667 = -8.353309391 Reorder the terms: -4.666666667 + x = -8.353309391 Solving -4.666666667 + x = -8.353309391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = -8.353309391 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = -8.353309391 + 4.666666667 x = -8.353309391 + 4.666666667 Combine like terms: -8.353309391 + 4.666666667 = -3.686642724 x = -3.686642724 Simplifying x = -3.686642724Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.019976058, -3.686642724}
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