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Simplifying 4x2 + 8x + 6 + -5x2 + 2 = 0 Reorder the terms: 6 + 2 + 8x + 4x2 + -5x2 = 0 Combine like terms: 6 + 2 = 8 8 + 8x + 4x2 + -5x2 = 0 Combine like terms: 4x2 + -5x2 = -1x2 8 + 8x + -1x2 = 0 Solving 8 + 8x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -8x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -8x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -8x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -8x + x2 = 0 + 8 -8x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -8x + x2 = 8 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 8 + 16 Reorder the terms: 16 + -8x + x2 = 8 + 16 Combine like terms: 8 + 16 = 24 16 + -8x + x2 = 24 Factor a perfect square on the left side: (x + -4)(x + -4) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -4) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -4 = 4.898979486 Simplifying x + -4 = 4.898979486 Reorder the terms: -4 + x = 4.898979486 Solving -4 + x = 4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.898979486 + 4 x = 4.898979486 + 4 Combine like terms: 4.898979486 + 4 = 8.898979486 x = 8.898979486 Simplifying x = 8.898979486Subproblem 2
x + -4 = -4.898979486 Simplifying x + -4 = -4.898979486 Reorder the terms: -4 + x = -4.898979486 Solving -4 + x = -4.898979486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.898979486 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.898979486 + 4 x = -4.898979486 + 4 Combine like terms: -4.898979486 + 4 = -0.898979486 x = -0.898979486 Simplifying x = -0.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.898979486, -0.898979486}
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