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Simplifying 4x2 + 7x = 189 Reorder the terms: 7x + 4x2 = 189 Solving 7x + 4x2 = 189 Solving for variable 'x'. Reorder the terms: -189 + 7x + 4x2 = 189 + -189 Combine like terms: 189 + -189 = 0 -189 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -47.25 + 1.75x + x2 = 0 Move the constant term to the right: Add '47.25' to each side of the equation. -47.25 + 1.75x + 47.25 + x2 = 0 + 47.25 Reorder the terms: -47.25 + 47.25 + 1.75x + x2 = 0 + 47.25 Combine like terms: -47.25 + 47.25 = 0.00 0.00 + 1.75x + x2 = 0 + 47.25 1.75x + x2 = 0 + 47.25 Combine like terms: 0 + 47.25 = 47.25 1.75x + x2 = 47.25 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 = 47.25 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 47.25 + 0.765625 Combine like terms: 47.25 + 0.765625 = 48.015625 0.765625 + 1.75x + x2 = 48.015625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 48.015625 Calculate the square root of the right side: 6.929330776 Break this problem into two subproblems by setting (x + 0.875) equal to 6.929330776 and -6.929330776.Subproblem 1
x + 0.875 = 6.929330776 Simplifying x + 0.875 = 6.929330776 Reorder the terms: 0.875 + x = 6.929330776 Solving 0.875 + x = 6.929330776 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 = 6.929330776 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 6.929330776 + -0.875 x = 6.929330776 + -0.875 Combine like terms: 6.929330776 + -0.875 = 6.054330776 x = 6.054330776 Simplifying x = 6.054330776Subproblem 2
x + 0.875 = -6.929330776 Simplifying x + 0.875 = -6.929330776 Reorder the terms: 0.875 + x = -6.929330776 Solving 0.875 + x = -6.929330776 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 = -6.929330776 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -6.929330776 + -0.875 x = -6.929330776 + -0.875 Combine like terms: -6.929330776 + -0.875 = -7.804330776 x = -7.804330776 Simplifying x = -7.804330776Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.054330776, -7.804330776}
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