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Simplifying 4x2 + -1x + 4 = x + 7 Reorder the terms: 4 + -1x + 4x2 = x + 7 Reorder the terms: 4 + -1x + 4x2 = 7 + x Solving 4 + -1x + 4x2 = 7 + x Solving for variable 'x'. Reorder the terms: 4 + -7 + -1x + -1x + 4x2 = 7 + x + -7 + -1x Combine like terms: 4 + -7 = -3 -3 + -1x + -1x + 4x2 = 7 + x + -7 + -1x Combine like terms: -1x + -1x = -2x -3 + -2x + 4x2 = 7 + x + -7 + -1x Reorder the terms: -3 + -2x + 4x2 = 7 + -7 + x + -1x Combine like terms: 7 + -7 = 0 -3 + -2x + 4x2 = 0 + x + -1x -3 + -2x + 4x2 = x + -1x Combine like terms: x + -1x = 0 -3 + -2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.5x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.5x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.5x + x2 = 0 + 0.75 -0.5x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.5x + x2 = 0.75 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.75 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.75 + 0.0625 Combine like terms: 0.75 + 0.0625 = 0.8125 0.0625 + -0.5x + x2 = 0.8125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (x + -0.25) equal to 0.901387819 and -0.901387819.Subproblem 1
x + -0.25 = 0.901387819 Simplifying x + -0.25 = 0.901387819 Reorder the terms: -0.25 + x = 0.901387819 Solving -0.25 + x = 0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.901387819 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.901387819 + 0.25 x = 0.901387819 + 0.25 Combine like terms: 0.901387819 + 0.25 = 1.151387819 x = 1.151387819 Simplifying x = 1.151387819Subproblem 2
x + -0.25 = -0.901387819 Simplifying x + -0.25 = -0.901387819 Reorder the terms: -0.25 + x = -0.901387819 Solving -0.25 + x = -0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.901387819 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.901387819 + 0.25 x = -0.901387819 + 0.25 Combine like terms: -0.901387819 + 0.25 = -0.651387819 x = -0.651387819 Simplifying x = -0.651387819Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.151387819, -0.651387819}
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