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Simplifying (x + 1)(2x + -5) + 8x2 + -7 = 0 Reorder the terms: (1 + x)(2x + -5) + 8x2 + -7 = 0 Reorder the terms: (1 + x)(-5 + 2x) + 8x2 + -7 = 0 Multiply (1 + x) * (-5 + 2x) (1(-5 + 2x) + x(-5 + 2x)) + 8x2 + -7 = 0 ((-5 * 1 + 2x * 1) + x(-5 + 2x)) + 8x2 + -7 = 0 ((-5 + 2x) + x(-5 + 2x)) + 8x2 + -7 = 0 (-5 + 2x + (-5 * x + 2x * x)) + 8x2 + -7 = 0 (-5 + 2x + (-5x + 2x2)) + 8x2 + -7 = 0 Combine like terms: 2x + -5x = -3x (-5 + -3x + 2x2) + 8x2 + -7 = 0 Reorder the terms: -5 + -7 + -3x + 2x2 + 8x2 = 0 Combine like terms: -5 + -7 = -12 -12 + -3x + 2x2 + 8x2 = 0 Combine like terms: 2x2 + 8x2 = 10x2 -12 + -3x + 10x2 = 0 Solving -12 + -3x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.2 + -0.3x + x2 = 0.0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.3x + 1.2 + x2 = 0.0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.3x + x2 = 0.0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.3x + x2 = 0.0 + 1.2 -0.3x + x2 = 0.0 + 1.2 Combine like terms: 0.0 + 1.2 = 1.2 -0.3x + x2 = 1.2 The x term is -0.3x. Take half its coefficient (-0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. -0.3x + 0.0225 + x2 = 1.2 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = 1.2 + 0.0225 Combine like terms: 1.2 + 0.0225 = 1.2225 0.0225 + -0.3x + x2 = 1.2225 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 1.2225 Calculate the square root of the right side: 1.105667219 Break this problem into two subproblems by setting (x + -0.15) equal to 1.105667219 and -1.105667219.Subproblem 1
x + -0.15 = 1.105667219 Simplifying x + -0.15 = 1.105667219 Reorder the terms: -0.15 + x = 1.105667219 Solving -0.15 + x = 1.105667219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = 1.105667219 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 1.105667219 + 0.15 x = 1.105667219 + 0.15 Combine like terms: 1.105667219 + 0.15 = 1.255667219 x = 1.255667219 Simplifying x = 1.255667219Subproblem 2
x + -0.15 = -1.105667219 Simplifying x + -0.15 = -1.105667219 Reorder the terms: -0.15 + x = -1.105667219 Solving -0.15 + x = -1.105667219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.15' to each side of the equation. -0.15 + 0.15 + x = -1.105667219 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -1.105667219 + 0.15 x = -1.105667219 + 0.15 Combine like terms: -1.105667219 + 0.15 = -0.955667219 x = -0.955667219 Simplifying x = -0.955667219Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.255667219, -0.955667219}
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