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Simplifying 8x + -11 = 5x(2x + 6) Reorder the terms: -11 + 8x = 5x(2x + 6) Reorder the terms: -11 + 8x = 5x(6 + 2x) -11 + 8x = (6 * 5x + 2x * 5x) -11 + 8x = (30x + 10x2) Solving -11 + 8x = 30x + 10x2 Solving for variable 'x'. Combine like terms: 8x + -30x = -22x -11 + -22x + -10x2 = 30x + 10x2 + -30x + -10x2 Reorder the terms: -11 + -22x + -10x2 = 30x + -30x + 10x2 + -10x2 Combine like terms: 30x + -30x = 0 -11 + -22x + -10x2 = 0 + 10x2 + -10x2 -11 + -22x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -11 + -22x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 22x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 22x + 10x2)' equal to zero and attempt to solve: Simplifying 11 + 22x + 10x2 = 0 Solving 11 + 22x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.1 + 2.2x + x2 = 0.0 Move the constant term to the right: Add '-1.1' to each side of the equation. 1.1 + 2.2x + -1.1 + x2 = 0.0 + -1.1 Reorder the terms: 1.1 + -1.1 + 2.2x + x2 = 0.0 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + 2.2x + x2 = 0.0 + -1.1 2.2x + x2 = 0.0 + -1.1 Combine like terms: 0.0 + -1.1 = -1.1 2.2x + x2 = -1.1 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = -1.1 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = -1.1 + 1.21 Combine like terms: -1.1 + 1.21 = 0.11 1.21 + 2.2x + x2 = 0.11 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 0.11 Calculate the square root of the right side: 0.331662479 Break this problem into two subproblems by setting (x + 1.1) equal to 0.331662479 and -0.331662479.Subproblem 1
x + 1.1 = 0.331662479 Simplifying x + 1.1 = 0.331662479 Reorder the terms: 1.1 + x = 0.331662479 Solving 1.1 + x = 0.331662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 0.331662479 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 0.331662479 + -1.1 x = 0.331662479 + -1.1 Combine like terms: 0.331662479 + -1.1 = -0.768337521 x = -0.768337521 Simplifying x = -0.768337521Subproblem 2
x + 1.1 = -0.331662479 Simplifying x + 1.1 = -0.331662479 Reorder the terms: 1.1 + x = -0.331662479 Solving 1.1 + x = -0.331662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -0.331662479 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -0.331662479 + -1.1 x = -0.331662479 + -1.1 Combine like terms: -0.331662479 + -1.1 = -1.431662479 x = -1.431662479 Simplifying x = -1.431662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.768337521, -1.431662479}Solution
x = {-0.768337521, -1.431662479}
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