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Simplifying 4x2 + 7x = 9 Reorder the terms: 7x + 4x2 = 9 Solving 7x + 4x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 7x + 4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 1.75x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 1.75x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 1.75x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 1.75x + x2 = 0 + 2.25 1.75x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 1.75x + x2 = 2.25 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 = 2.25 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 2.25 + 0.765625 Combine like terms: 2.25 + 0.765625 = 3.015625 0.765625 + 1.75x + x2 = 3.015625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 3.015625 Calculate the square root of the right side: 1.736555499 Break this problem into two subproblems by setting (x + 0.875) equal to 1.736555499 and -1.736555499.Subproblem 1
x + 0.875 = 1.736555499 Simplifying x + 0.875 = 1.736555499 Reorder the terms: 0.875 + x = 1.736555499 Solving 0.875 + x = 1.736555499 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 = 1.736555499 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.736555499 + -0.875 x = 1.736555499 + -0.875 Combine like terms: 1.736555499 + -0.875 = 0.861555499 x = 0.861555499 Simplifying x = 0.861555499Subproblem 2
x + 0.875 = -1.736555499 Simplifying x + 0.875 = -1.736555499 Reorder the terms: 0.875 + x = -1.736555499 Solving 0.875 + x = -1.736555499 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 = -1.736555499 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.736555499 + -0.875 x = -1.736555499 + -0.875 Combine like terms: -1.736555499 + -0.875 = -2.611555499 x = -2.611555499 Simplifying x = -2.611555499Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.861555499, -2.611555499}
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