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Simplifying 8x2 + 24x = 4x2 + 15 Reorder the terms: 24x + 8x2 = 4x2 + 15 Reorder the terms: 24x + 8x2 = 15 + 4x2 Solving 24x + 8x2 = 15 + 4x2 Solving for variable 'x'. Reorder the terms: -15 + 24x + 8x2 + -4x2 = 15 + 4x2 + -15 + -4x2 Combine like terms: 8x2 + -4x2 = 4x2 -15 + 24x + 4x2 = 15 + 4x2 + -15 + -4x2 Reorder the terms: -15 + 24x + 4x2 = 15 + -15 + 4x2 + -4x2 Combine like terms: 15 + -15 = 0 -15 + 24x + 4x2 = 0 + 4x2 + -4x2 -15 + 24x + 4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -15 + 24x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 6x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 6x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 6x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 6x + x2 = 0 + 3.75 6x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 6x + x2 = 3.75 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 3.75 + 9 Reorder the terms: 9 + 6x + x2 = 3.75 + 9 Combine like terms: 3.75 + 9 = 12.75 9 + 6x + x2 = 12.75 Factor a perfect square on the left side: (x + 3)(x + 3) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (x + 3) equal to 3.570714214 and -3.570714214.Subproblem 1
x + 3 = 3.570714214 Simplifying x + 3 = 3.570714214 Reorder the terms: 3 + x = 3.570714214 Solving 3 + x = 3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.570714214 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.570714214 + -3 x = 3.570714214 + -3 Combine like terms: 3.570714214 + -3 = 0.570714214 x = 0.570714214 Simplifying x = 0.570714214Subproblem 2
x + 3 = -3.570714214 Simplifying x + 3 = -3.570714214 Reorder the terms: 3 + x = -3.570714214 Solving 3 + x = -3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.570714214 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.570714214 + -3 x = -3.570714214 + -3 Combine like terms: -3.570714214 + -3 = -6.570714214 x = -6.570714214 Simplifying x = -6.570714214Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.570714214, -6.570714214}
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