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Simplifying -16x2 + -10x + 378 = 0 Reorder the terms: 378 + -10x + -16x2 = 0 Solving 378 + -10x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(189 + -5x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(189 + -5x + -8x2)' equal to zero and attempt to solve: Simplifying 189 + -5x + -8x2 = 0 Solving 189 + -5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -23.625 + 0.625x + x2 = 0 Move the constant term to the right: Add '23.625' to each side of the equation. -23.625 + 0.625x + 23.625 + x2 = 0 + 23.625 Reorder the terms: -23.625 + 23.625 + 0.625x + x2 = 0 + 23.625 Combine like terms: -23.625 + 23.625 = 0.000 0.000 + 0.625x + x2 = 0 + 23.625 0.625x + x2 = 0 + 23.625 Combine like terms: 0 + 23.625 = 23.625 0.625x + x2 = 23.625 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 23.625 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 23.625 + 0.09765625 Combine like terms: 23.625 + 0.09765625 = 23.72265625 0.09765625 + 0.625x + x2 = 23.72265625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 23.72265625 Calculate the square root of the right side: 4.870590955 Break this problem into two subproblems by setting (x + 0.3125) equal to 4.870590955 and -4.870590955.Subproblem 1
x + 0.3125 = 4.870590955 Simplifying x + 0.3125 = 4.870590955 Reorder the terms: 0.3125 + x = 4.870590955 Solving 0.3125 + x = 4.870590955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 4.870590955 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 4.870590955 + -0.3125 x = 4.870590955 + -0.3125 Combine like terms: 4.870590955 + -0.3125 = 4.558090955 x = 4.558090955 Simplifying x = 4.558090955Subproblem 2
x + 0.3125 = -4.870590955 Simplifying x + 0.3125 = -4.870590955 Reorder the terms: 0.3125 + x = -4.870590955 Solving 0.3125 + x = -4.870590955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -4.870590955 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -4.870590955 + -0.3125 x = -4.870590955 + -0.3125 Combine like terms: -4.870590955 + -0.3125 = -5.183090955 x = -5.183090955 Simplifying x = -5.183090955Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.558090955, -5.183090955}Solution
x = {4.558090955, -5.183090955}
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