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Simplifying 2.823520 = 4x2 + 8x Reorder the terms: 2.823520 = 8x + 4x2 Solving 2.823520 = 8x + 4x2 Solving for variable 'x'. Reorder the terms: 2.823520 + -8x + -4x2 = 8x + -8x + 4x2 + -4x2 Combine like terms: 8x + -8x = 0 2.823520 + -8x + -4x2 = 0 + 4x2 + -4x2 2.823520 + -8x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 2.823520 + -8x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.70588 + 2x + x2 = 0 Move the constant term to the right: Add '0.70588' to each side of the equation. -0.70588 + 2x + 0.70588 + x2 = 0 + 0.70588 Reorder the terms: -0.70588 + 0.70588 + 2x + x2 = 0 + 0.70588 Combine like terms: -0.70588 + 0.70588 = 0.00000 0.00000 + 2x + x2 = 0 + 0.70588 2x + x2 = 0 + 0.70588 Combine like terms: 0 + 0.70588 = 0.70588 2x + x2 = 0.70588 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.70588 + 1 Reorder the terms: 1 + 2x + x2 = 0.70588 + 1 Combine like terms: 0.70588 + 1 = 1.70588 1 + 2x + x2 = 1.70588 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.70588 Calculate the square root of the right side: 1.306093412 Break this problem into two subproblems by setting (x + 1) equal to 1.306093412 and -1.306093412.Subproblem 1
x + 1 = 1.306093412 Simplifying x + 1 = 1.306093412 Reorder the terms: 1 + x = 1.306093412 Solving 1 + x = 1.306093412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.306093412 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.306093412 + -1 x = 1.306093412 + -1 Combine like terms: 1.306093412 + -1 = 0.306093412 x = 0.306093412 Simplifying x = 0.306093412Subproblem 2
x + 1 = -1.306093412 Simplifying x + 1 = -1.306093412 Reorder the terms: 1 + x = -1.306093412 Solving 1 + x = -1.306093412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.306093412 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.306093412 + -1 x = -1.306093412 + -1 Combine like terms: -1.306093412 + -1 = -2.306093412 x = -2.306093412 Simplifying x = -2.306093412Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.306093412, -2.306093412}
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