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Simplifying -4t2 + 5t + 7 = 0 Reorder the terms: 7 + 5t + -4t2 = 0 Solving 7 + 5t + -4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + -1.25t + t2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -1.25t + 1.75 + t2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -1.25t + t2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -1.25t + t2 = 0 + 1.75 -1.25t + t2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -1.25t + t2 = 1.75 The t term is -1.25t. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25t + 0.390625 + t2 = 1.75 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = 1.75 + 0.390625 Combine like terms: 1.75 + 0.390625 = 2.140625 0.390625 + -1.25t + t2 = 2.140625 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (t + -0.625) equal to 1.463087489 and -1.463087489.Subproblem 1
t + -0.625 = 1.463087489 Simplifying t + -0.625 = 1.463087489 Reorder the terms: -0.625 + t = 1.463087489 Solving -0.625 + t = 1.463087489 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = 1.463087489 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 1.463087489 + 0.625 t = 1.463087489 + 0.625 Combine like terms: 1.463087489 + 0.625 = 2.088087489 t = 2.088087489 Simplifying t = 2.088087489Subproblem 2
t + -0.625 = -1.463087489 Simplifying t + -0.625 = -1.463087489 Reorder the terms: -0.625 + t = -1.463087489 Solving -0.625 + t = -1.463087489 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = -1.463087489 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -1.463087489 + 0.625 t = -1.463087489 + 0.625 Combine like terms: -1.463087489 + 0.625 = -0.838087489 t = -0.838087489 Simplifying t = -0.838087489Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.088087489, -0.838087489}
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