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Simplifying 5x2 + -42x + -32 = 0 Reorder the terms: -32 + -42x + 5x2 = 0 Solving -32 + -42x + 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'. -6.4 + -8.4x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + -8.4x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + -8.4x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + -8.4x + x2 = 0 + 6.4 -8.4x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 -8.4x + x2 = 6.4 The x term is -8.4x. Take half its coefficient (-4.2). Square it (17.64) and add it to both sides. Add '17.64' to each side of the equation. -8.4x + 17.64 + x2 = 6.4 + 17.64 Reorder the terms: 17.64 + -8.4x + x2 = 6.4 + 17.64 Combine like terms: 6.4 + 17.64 = 24.04 17.64 + -8.4x + x2 = 24.04 Factor a perfect square on the left side: (x + -4.2)(x + -4.2) = 24.04 Calculate the square root of the right side: 4.903060269 Break this problem into two subproblems by setting (x + -4.2) equal to 4.903060269 and -4.903060269.Subproblem 1
x + -4.2 = 4.903060269 Simplifying x + -4.2 = 4.903060269 Reorder the terms: -4.2 + x = 4.903060269 Solving -4.2 + x = 4.903060269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.2' to each side of the equation. -4.2 + 4.2 + x = 4.903060269 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + x = 4.903060269 + 4.2 x = 4.903060269 + 4.2 Combine like terms: 4.903060269 + 4.2 = 9.103060269 x = 9.103060269 Simplifying x = 9.103060269Subproblem 2
x + -4.2 = -4.903060269 Simplifying x + -4.2 = -4.903060269 Reorder the terms: -4.2 + x = -4.903060269 Solving -4.2 + x = -4.903060269 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.2' to each side of the equation. -4.2 + 4.2 + x = -4.903060269 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + x = -4.903060269 + 4.2 x = -4.903060269 + 4.2 Combine like terms: -4.903060269 + 4.2 = -0.703060269 x = -0.703060269 Simplifying x = -0.703060269Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.103060269, -0.703060269}
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