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Simplifying 4x2 + -5 = 7x Reorder the terms: -5 + 4x2 = 7x Solving -5 + 4x2 = 7x Solving for variable 'x'. Reorder the terms: -5 + -7x + 4x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -5 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -1.75x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -1.75x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -1.75x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -1.75x + x2 = 0 + 1.25 -1.75x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -1.75x + x2 = 1.25 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 1.25 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 1.25 + 0.765625 Combine like terms: 1.25 + 0.765625 = 2.015625 0.765625 + -1.75x + x2 = 2.015625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (x + -0.875) equal to 1.419727086 and -1.419727086.Subproblem 1
x + -0.875 = 1.419727086 Simplifying x + -0.875 = 1.419727086 Reorder the terms: -0.875 + x = 1.419727086 Solving -0.875 + x = 1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 1.419727086 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.419727086 + 0.875 x = 1.419727086 + 0.875 Combine like terms: 1.419727086 + 0.875 = 2.294727086 x = 2.294727086 Simplifying x = 2.294727086Subproblem 2
x + -0.875 = -1.419727086 Simplifying x + -0.875 = -1.419727086 Reorder the terms: -0.875 + x = -1.419727086 Solving -0.875 + x = -1.419727086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -1.419727086 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.419727086 + 0.875 x = -1.419727086 + 0.875 Combine like terms: -1.419727086 + 0.875 = -0.544727086 x = -0.544727086 Simplifying x = -0.544727086Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.294727086, -0.544727086}
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