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Simplifying (-4x2 + x + 5) + -1(x2 + 2x + 3) = 0 Reorder the terms: (5 + x + -4x2) + -1(x2 + 2x + 3) = 0 Remove parenthesis around (5 + x + -4x2) 5 + x + -4x2 + -1(x2 + 2x + 3) = 0 Reorder the terms: 5 + x + -4x2 + -1(3 + 2x + x2) = 0 5 + x + -4x2 + (3 * -1 + 2x * -1 + x2 * -1) = 0 5 + x + -4x2 + (-3 + -2x + -1x2) = 0 Reorder the terms: 5 + -3 + x + -2x + -4x2 + -1x2 = 0 Combine like terms: 5 + -3 = 2 2 + x + -2x + -4x2 + -1x2 = 0 Combine like terms: x + -2x = -1x 2 + -1x + -4x2 + -1x2 = 0 Combine like terms: -4x2 + -1x2 = -5x2 2 + -1x + -5x2 = 0 Solving 2 + -1x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + 0.2x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.2x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.2x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.2x + x2 = 0 + 0.4 0.2x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.2x + x2 = 0.4 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 0.4 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.4 + 0.01 Combine like terms: 0.4 + 0.01 = 0.41 0.01 + 0.2x + x2 = 0.41 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + 0.1) equal to 0.640312424 and -0.640312424.Subproblem 1
x + 0.1 = 0.640312424 Simplifying x + 0.1 = 0.640312424 Reorder the terms: 0.1 + x = 0.640312424 Solving 0.1 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.640312424 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.640312424 + -0.1 x = 0.640312424 + -0.1 Combine like terms: 0.640312424 + -0.1 = 0.540312424 x = 0.540312424 Simplifying x = 0.540312424Subproblem 2
x + 0.1 = -0.640312424 Simplifying x + 0.1 = -0.640312424 Reorder the terms: 0.1 + x = -0.640312424 Solving 0.1 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.640312424 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.640312424 + -0.1 x = -0.640312424 + -0.1 Combine like terms: -0.640312424 + -0.1 = -0.740312424 x = -0.740312424 Simplifying x = -0.740312424Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.540312424, -0.740312424}
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