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Simplifying 5x + 7 = 3x(x + 9) + -20 Reorder the terms: 7 + 5x = 3x(x + 9) + -20 Reorder the terms: 7 + 5x = 3x(9 + x) + -20 7 + 5x = (9 * 3x + x * 3x) + -20 7 + 5x = (27x + 3x2) + -20 Reorder the terms: 7 + 5x = -20 + 27x + 3x2 Solving 7 + 5x = -20 + 27x + 3x2 Solving for variable 'x'. Reorder the terms: 7 + 20 + 5x + -27x + -3x2 = -20 + 27x + 3x2 + 20 + -27x + -3x2 Combine like terms: 7 + 20 = 27 27 + 5x + -27x + -3x2 = -20 + 27x + 3x2 + 20 + -27x + -3x2 Combine like terms: 5x + -27x = -22x 27 + -22x + -3x2 = -20 + 27x + 3x2 + 20 + -27x + -3x2 Reorder the terms: 27 + -22x + -3x2 = -20 + 20 + 27x + -27x + 3x2 + -3x2 Combine like terms: -20 + 20 = 0 27 + -22x + -3x2 = 0 + 27x + -27x + 3x2 + -3x2 27 + -22x + -3x2 = 27x + -27x + 3x2 + -3x2 Combine like terms: 27x + -27x = 0 27 + -22x + -3x2 = 0 + 3x2 + -3x2 27 + -22x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 27 + -22x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -9 + 7.333333333x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 7.333333333x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 7.333333333x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 7.333333333x + x2 = 0 + 9 7.333333333x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 7.333333333x + x2 = 9 The x term is 7.333333333x. Take half its coefficient (3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. 7.333333333x + 13.44444445 + x2 = 9 + 13.44444445 Reorder the terms: 13.44444445 + 7.333333333x + x2 = 9 + 13.44444445 Combine like terms: 9 + 13.44444445 = 22.44444445 13.44444445 + 7.333333333x + x2 = 22.44444445 Factor a perfect square on the left side: (x + 3.666666667)(x + 3.666666667) = 22.44444445 Calculate the square root of the right side: 4.737556802 Break this problem into two subproblems by setting (x + 3.666666667) equal to 4.737556802 and -4.737556802.Subproblem 1
x + 3.666666667 = 4.737556802 Simplifying x + 3.666666667 = 4.737556802 Reorder the terms: 3.666666667 + x = 4.737556802 Solving 3.666666667 + x = 4.737556802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = 4.737556802 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = 4.737556802 + -3.666666667 x = 4.737556802 + -3.666666667 Combine like terms: 4.737556802 + -3.666666667 = 1.070890135 x = 1.070890135 Simplifying x = 1.070890135Subproblem 2
x + 3.666666667 = -4.737556802 Simplifying x + 3.666666667 = -4.737556802 Reorder the terms: 3.666666667 + x = -4.737556802 Solving 3.666666667 + x = -4.737556802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = -4.737556802 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = -4.737556802 + -3.666666667 x = -4.737556802 + -3.666666667 Combine like terms: -4.737556802 + -3.666666667 = -8.404223469 x = -8.404223469 Simplifying x = -8.404223469Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.070890135, -8.404223469}
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