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Simplifying 760 = (2x + -4)(x) Reorder the terms: 760 = (-4 + 2x)(x) Reorder the terms for easier multiplication: 760 = x(-4 + 2x) 760 = (-4 * x + 2x * x) 760 = (-4x + 2x2) Solving 760 = -4x + 2x2 Solving for variable 'x'. Reorder the terms: 760 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2 Combine like terms: -4x + 4x = 0 760 + 4x + -2x2 = 0 + 2x2 + -2x2 760 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 760 + 4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(380 + 2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(380 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 380 + 2x + -1x2 = 0 Solving 380 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -380 + -2x + x2 = 0 Move the constant term to the right: Add '380' to each side of the equation. -380 + -2x + 380 + x2 = 0 + 380 Reorder the terms: -380 + 380 + -2x + x2 = 0 + 380 Combine like terms: -380 + 380 = 0 0 + -2x + x2 = 0 + 380 -2x + x2 = 0 + 380 Combine like terms: 0 + 380 = 380 -2x + x2 = 380 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 = 380 + 1 Reorder the terms: 1 + -2x + x2 = 380 + 1 Combine like terms: 380 + 1 = 381 1 + -2x + x2 = 381 Factor a perfect square on the left side: (x + -1)(x + -1) = 381 Calculate the square root of the right side: 19.519221296 Break this problem into two subproblems by setting (x + -1) equal to 19.519221296 and -19.519221296.Subproblem 1
x + -1 = 19.519221296 Simplifying x + -1 = 19.519221296 Reorder the terms: -1 + x = 19.519221296 Solving -1 + x = 19.519221296 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 = 19.519221296 + 1 Combine like terms: -1 + 1 = 0 0 + x = 19.519221296 + 1 x = 19.519221296 + 1 Combine like terms: 19.519221296 + 1 = 20.519221296 x = 20.519221296 Simplifying x = 20.519221296Subproblem 2
x + -1 = -19.519221296 Simplifying x + -1 = -19.519221296 Reorder the terms: -1 + x = -19.519221296 Solving -1 + x = -19.519221296 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 = -19.519221296 + 1 Combine like terms: -1 + 1 = 0 0 + x = -19.519221296 + 1 x = -19.519221296 + 1 Combine like terms: -19.519221296 + 1 = -18.519221296 x = -18.519221296 Simplifying x = -18.519221296Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.519221296, -18.519221296}Solution
x = {20.519221296, -18.519221296}
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