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Simplifying 8x(3x + 7) = 33 Reorder the terms: 8x(7 + 3x) = 33 (7 * 8x + 3x * 8x) = 33 (56x + 24x2) = 33 Solving 56x + 24x2 = 33 Solving for variable 'x'. Reorder the terms: -33 + 56x + 24x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + 56x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -1.375 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 2.333333333x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 2.333333333x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 2.333333333x + x2 = 0 + 1.375 2.333333333x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 2.333333333x + x2 = 1.375 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 1.375 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 1.375 + 1.361111112 Combine like terms: 1.375 + 1.361111112 = 2.736111112 1.361111112 + 2.333333333x + x2 = 2.736111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 2.736111112 Calculate the square root of the right side: 1.654119437 Break this problem into two subproblems by setting (x + 1.166666667) equal to 1.654119437 and -1.654119437.Subproblem 1
x + 1.166666667 = 1.654119437 Simplifying x + 1.166666667 = 1.654119437 Reorder the terms: 1.166666667 + x = 1.654119437 Solving 1.166666667 + x = 1.654119437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 1.654119437 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 1.654119437 + -1.166666667 x = 1.654119437 + -1.166666667 Combine like terms: 1.654119437 + -1.166666667 = 0.48745277 x = 0.48745277 Simplifying x = 0.48745277Subproblem 2
x + 1.166666667 = -1.654119437 Simplifying x + 1.166666667 = -1.654119437 Reorder the terms: 1.166666667 + x = -1.654119437 Solving 1.166666667 + x = -1.654119437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -1.654119437 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -1.654119437 + -1.166666667 x = -1.654119437 + -1.166666667 Combine like terms: -1.654119437 + -1.166666667 = -2.820786104 x = -2.820786104 Simplifying x = -2.820786104Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.48745277, -2.820786104}
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