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Simplifying 4x + -3x(x + -8) = -18 Reorder the terms: 4x + -3x(-8 + x) = -18 4x + (-8 * -3x + x * -3x) = -18 4x + (24x + -3x2) = -18 Combine like terms: 4x + 24x = 28x 28x + -3x2 = -18 Solving 28x + -3x2 = -18 Solving for variable 'x'. Reorder the terms: 18 + 28x + -3x2 = -18 + 18 Combine like terms: -18 + 18 = 0 18 + 28x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -6 + -9.333333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -9.333333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -9.333333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -9.333333333x + x2 = 0 + 6 -9.333333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -9.333333333x + x2 = 6 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 = 6 + 21.77777778 Reorder the terms: 21.77777778 + -9.333333333x + x2 = 6 + 21.77777778 Combine like terms: 6 + 21.77777778 = 27.77777778 21.77777778 + -9.333333333x + x2 = 27.77777778 Factor a perfect square on the left side: (x + -4.666666667)(x + -4.666666667) = 27.77777778 Calculate the square root of the right side: 5.270462767 Break this problem into two subproblems by setting (x + -4.666666667) equal to 5.270462767 and -5.270462767.Subproblem 1
x + -4.666666667 = 5.270462767 Simplifying x + -4.666666667 = 5.270462767 Reorder the terms: -4.666666667 + x = 5.270462767 Solving -4.666666667 + x = 5.270462767 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 = 5.270462767 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = 5.270462767 + 4.666666667 x = 5.270462767 + 4.666666667 Combine like terms: 5.270462767 + 4.666666667 = 9.937129434 x = 9.937129434 Simplifying x = 9.937129434Subproblem 2
x + -4.666666667 = -5.270462767 Simplifying x + -4.666666667 = -5.270462767 Reorder the terms: -4.666666667 + x = -5.270462767 Solving -4.666666667 + x = -5.270462767 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 = -5.270462767 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = -5.270462767 + 4.666666667 x = -5.270462767 + 4.666666667 Combine like terms: -5.270462767 + 4.666666667 = -0.6037961 x = -0.6037961 Simplifying x = -0.6037961Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.937129434, -0.6037961}
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