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Simplifying 7x(3x + -8) = 32 Reorder the terms: 7x(-8 + 3x) = 32 (-8 * 7x + 3x * 7x) = 32 (-56x + 21x2) = 32 Solving -56x + 21x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + -56x + 21x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -56x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -1.523809524 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '1.523809524' to each side of the equation. -1.523809524 + -2.666666667x + 1.523809524 + x2 = 0 + 1.523809524 Reorder the terms: -1.523809524 + 1.523809524 + -2.666666667x + x2 = 0 + 1.523809524 Combine like terms: -1.523809524 + 1.523809524 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + 1.523809524 -2.666666667x + x2 = 0 + 1.523809524 Combine like terms: 0 + 1.523809524 = 1.523809524 -2.666666667x + x2 = 1.523809524 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 1.523809524 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 1.523809524 + 1.777777780 Combine like terms: 1.523809524 + 1.777777780 = 3.301587304 1.777777780 + -2.666666667x + x2 = 3.301587304 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 3.301587304 Calculate the square root of the right side: 1.817027051 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.817027051 and -1.817027051.Subproblem 1
x + -1.333333334 = 1.817027051 Simplifying x + -1.333333334 = 1.817027051 Reorder the terms: -1.333333334 + x = 1.817027051 Solving -1.333333334 + x = 1.817027051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.817027051 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.817027051 + 1.333333334 x = 1.817027051 + 1.333333334 Combine like terms: 1.817027051 + 1.333333334 = 3.150360385 x = 3.150360385 Simplifying x = 3.150360385Subproblem 2
x + -1.333333334 = -1.817027051 Simplifying x + -1.333333334 = -1.817027051 Reorder the terms: -1.333333334 + x = -1.817027051 Solving -1.333333334 + x = -1.817027051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.817027051 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.817027051 + 1.333333334 x = -1.817027051 + 1.333333334 Combine like terms: -1.817027051 + 1.333333334 = -0.483693717 x = -0.483693717 Simplifying x = -0.483693717Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.150360385, -0.483693717}
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