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Simplifying [3x + 7][4x + -15] = 90 Reorder the terms: [7 + 3x][4x + -15] = 90 Reorder the terms: [7 + 3x][-15 + 4x] = 90 Multiply [7 + 3x] * [-15 + 4x] [7[-15 + 4x] + 3x * [-15 + 4x]] = 90 [[-15 * 7 + 4x * 7] + 3x * [-15 + 4x]] = 90 [[-105 + 28x] + 3x * [-15 + 4x]] = 90 [-105 + 28x + [-15 * 3x + 4x * 3x]] = 90 [-105 + 28x + [-45x + 12x2]] = 90 Combine like terms: 28x + -45x = -17x [-105 + -17x + 12x2] = 90 Solving -105 + -17x + 12x2 = 90 Solving for variable 'x'. Reorder the terms: -105 + -90 + -17x + 12x2 = 90 + -90 Combine like terms: -105 + -90 = -195 -195 + -17x + 12x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -195 + -17x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -16.25 + -1.416666667x + x2 = 0 Move the constant term to the right: Add '16.25' to each side of the equation. -16.25 + -1.416666667x + 16.25 + x2 = 0 + 16.25 Reorder the terms: -16.25 + 16.25 + -1.416666667x + x2 = 0 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + -1.416666667x + x2 = 0 + 16.25 -1.416666667x + x2 = 0 + 16.25 Combine like terms: 0 + 16.25 = 16.25 -1.416666667x + x2 = 16.25 The x term is -1.416666667x. Take half its coefficient (-0.7083333335). Square it (0.5017361113) and add it to both sides. Add '0.5017361113' to each side of the equation. -1.416666667x + 0.5017361113 + x2 = 16.25 + 0.5017361113 Reorder the terms: 0.5017361113 + -1.416666667x + x2 = 16.25 + 0.5017361113 Combine like terms: 16.25 + 0.5017361113 = 16.7517361113 0.5017361113 + -1.416666667x + x2 = 16.7517361113 Factor a perfect square on the left side: (x + -0.7083333335)(x + -0.7083333335) = 16.7517361113 Calculate the square root of the right side: 4.09288848 Break this problem into two subproblems by setting (x + -0.7083333335) equal to 4.09288848 and -4.09288848.Subproblem 1
x + -0.7083333335 = 4.09288848 Simplifying x + -0.7083333335 = 4.09288848 Reorder the terms: -0.7083333335 + x = 4.09288848 Solving -0.7083333335 + x = 4.09288848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + x = 4.09288848 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = 4.09288848 + 0.7083333335 x = 4.09288848 + 0.7083333335 Combine like terms: 4.09288848 + 0.7083333335 = 4.8012218135 x = 4.8012218135 Simplifying x = 4.8012218135Subproblem 2
x + -0.7083333335 = -4.09288848 Simplifying x + -0.7083333335 = -4.09288848 Reorder the terms: -0.7083333335 + x = -4.09288848 Solving -0.7083333335 + x = -4.09288848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7083333335' to each side of the equation. -0.7083333335 + 0.7083333335 + x = -4.09288848 + 0.7083333335 Combine like terms: -0.7083333335 + 0.7083333335 = 0.0000000000 0.0000000000 + x = -4.09288848 + 0.7083333335 x = -4.09288848 + 0.7083333335 Combine like terms: -4.09288848 + 0.7083333335 = -3.3845551465 x = -3.3845551465 Simplifying x = -3.3845551465Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.8012218135, -3.3845551465}
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