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Simplifying x = 4x2 + -5.25x + 2 Reorder the terms: x = 2 + -5.25x + 4x2 Solving x = 2 + -5.25x + 4x2 Solving for variable 'x'. Reorder the terms: -2 + x + 5.25x + -4x2 = 2 + -5.25x + 4x2 + -2 + 5.25x + -4x2 Combine like terms: x + 5.25x = 6.25x -2 + 6.25x + -4x2 = 2 + -5.25x + 4x2 + -2 + 5.25x + -4x2 Reorder the terms: -2 + 6.25x + -4x2 = 2 + -2 + -5.25x + 5.25x + 4x2 + -4x2 Combine like terms: 2 + -2 = 0 -2 + 6.25x + -4x2 = 0 + -5.25x + 5.25x + 4x2 + -4x2 -2 + 6.25x + -4x2 = -5.25x + 5.25x + 4x2 + -4x2 Combine like terms: -5.25x + 5.25x = 0.00 -2 + 6.25x + -4x2 = 0.00 + 4x2 + -4x2 -2 + 6.25x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -2 + 6.25x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.5 + -1.5625x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.5625x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.5625x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.5625x + x2 = 0 + -0.5 -1.5625x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.5625x + x2 = -0.5 The x term is -1.5625x. Take half its coefficient (-0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. -1.5625x + 0.6103515625 + x2 = -0.5 + 0.6103515625 Reorder the terms: 0.6103515625 + -1.5625x + x2 = -0.5 + 0.6103515625 Combine like terms: -0.5 + 0.6103515625 = 0.1103515625 0.6103515625 + -1.5625x + x2 = 0.1103515625 Factor a perfect square on the left side: (x + -0.78125)(x + -0.78125) = 0.1103515625 Calculate the square root of the right side: 0.332192057 Break this problem into two subproblems by setting (x + -0.78125) equal to 0.332192057 and -0.332192057.Subproblem 1
x + -0.78125 = 0.332192057 Simplifying x + -0.78125 = 0.332192057 Reorder the terms: -0.78125 + x = 0.332192057 Solving -0.78125 + x = 0.332192057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + x = 0.332192057 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + x = 0.332192057 + 0.78125 x = 0.332192057 + 0.78125 Combine like terms: 0.332192057 + 0.78125 = 1.113442057 x = 1.113442057 Simplifying x = 1.113442057Subproblem 2
x + -0.78125 = -0.332192057 Simplifying x + -0.78125 = -0.332192057 Reorder the terms: -0.78125 + x = -0.332192057 Solving -0.78125 + x = -0.332192057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.78125' to each side of the equation. -0.78125 + 0.78125 + x = -0.332192057 + 0.78125 Combine like terms: -0.78125 + 0.78125 = 0.00000 0.00000 + x = -0.332192057 + 0.78125 x = -0.332192057 + 0.78125 Combine like terms: -0.332192057 + 0.78125 = 0.449057943 x = 0.449057943 Simplifying x = 0.449057943Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.113442057, 0.449057943}
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