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Simplifying 4x2 + 15x + -51 = 0 Reorder the terms: -51 + 15x + 4x2 = 0 Solving -51 + 15x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.75 + 3.75x + x2 = 0 Move the constant term to the right: Add '12.75' to each side of the equation. -12.75 + 3.75x + 12.75 + x2 = 0 + 12.75 Reorder the terms: -12.75 + 12.75 + 3.75x + x2 = 0 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + 3.75x + x2 = 0 + 12.75 3.75x + x2 = 0 + 12.75 Combine like terms: 0 + 12.75 = 12.75 3.75x + x2 = 12.75 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 12.75 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 12.75 + 3.515625 Combine like terms: 12.75 + 3.515625 = 16.265625 3.515625 + 3.75x + x2 = 16.265625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 16.265625 Calculate the square root of the right side: 4.033066451 Break this problem into two subproblems by setting (x + 1.875) equal to 4.033066451 and -4.033066451.Subproblem 1
x + 1.875 = 4.033066451 Simplifying x + 1.875 = 4.033066451 Reorder the terms: 1.875 + x = 4.033066451 Solving 1.875 + x = 4.033066451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 4.033066451 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 4.033066451 + -1.875 x = 4.033066451 + -1.875 Combine like terms: 4.033066451 + -1.875 = 2.158066451 x = 2.158066451 Simplifying x = 2.158066451Subproblem 2
x + 1.875 = -4.033066451 Simplifying x + 1.875 = -4.033066451 Reorder the terms: 1.875 + x = -4.033066451 Solving 1.875 + x = -4.033066451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -4.033066451 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -4.033066451 + -1.875 x = -4.033066451 + -1.875 Combine like terms: -4.033066451 + -1.875 = -5.908066451 x = -5.908066451 Simplifying x = -5.908066451Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.158066451, -5.908066451}
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