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Simplifying 2x + 4 + -5x(x + -5) = 5x Reorder the terms: 2x + 4 + -5x(-5 + x) = 5x 2x + 4 + (-5 * -5x + x * -5x) = 5x 2x + 4 + (25x + -5x2) = 5x Reorder the terms: 4 + 2x + 25x + -5x2 = 5x Combine like terms: 2x + 25x = 27x 4 + 27x + -5x2 = 5x Solving 4 + 27x + -5x2 = 5x Solving for variable 'x'. Reorder the terms: 4 + 27x + -5x + -5x2 = 5x + -5x Combine like terms: 27x + -5x = 22x 4 + 22x + -5x2 = 5x + -5x Combine like terms: 5x + -5x = 0 4 + 22x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.8 + -4.4x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -4.4x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -4.4x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -4.4x + x2 = 0 + 0.8 -4.4x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -4.4x + x2 = 0.8 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = 0.8 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = 0.8 + 4.84 Combine like terms: 0.8 + 4.84 = 5.64 4.84 + -4.4x + x2 = 5.64 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 5.64 Calculate the square root of the right side: 2.374868417 Break this problem into two subproblems by setting (x + -2.2) equal to 2.374868417 and -2.374868417.Subproblem 1
x + -2.2 = 2.374868417 Simplifying x + -2.2 = 2.374868417 Reorder the terms: -2.2 + x = 2.374868417 Solving -2.2 + x = 2.374868417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 2.374868417 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 2.374868417 + 2.2 x = 2.374868417 + 2.2 Combine like terms: 2.374868417 + 2.2 = 4.574868417 x = 4.574868417 Simplifying x = 4.574868417Subproblem 2
x + -2.2 = -2.374868417 Simplifying x + -2.2 = -2.374868417 Reorder the terms: -2.2 + x = -2.374868417 Solving -2.2 + x = -2.374868417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -2.374868417 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -2.374868417 + 2.2 x = -2.374868417 + 2.2 Combine like terms: -2.374868417 + 2.2 = -0.174868417 x = -0.174868417 Simplifying x = -0.174868417Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.574868417, -0.174868417}
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