40t^2+80t-70=0

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Solution for 40t^2+80t-70=0 equation:


Simplifying
40t2 + 80t + -70 = 0

Reorder the terms:
-70 + 80t + 40t2 = 0

Solving
-70 + 80t + 40t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-7 + 8t + 4t2) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(-7 + 8t + 4t2)' equal to zero and attempt to solve: Simplifying -7 + 8t + 4t2 = 0 Solving -7 + 8t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + 2t + t2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 2t + 1.75 + t2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 2t + t2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 2t + t2 = 0 + 1.75 2t + t2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 2t + t2 = 1.75 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 1.75 + 1 Reorder the terms: 1 + 2t + t2 = 1.75 + 1 Combine like terms: 1.75 + 1 = 2.75 1 + 2t + t2 = 2.75 Factor a perfect square on the left side: (t + 1)(t + 1) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (t + 1) equal to 1.658312395 and -1.658312395.

Subproblem 1

t + 1 = 1.658312395 Simplifying t + 1 = 1.658312395 Reorder the terms: 1 + t = 1.658312395 Solving 1 + t = 1.658312395 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 1.658312395 + -1 Combine like terms: 1 + -1 = 0 0 + t = 1.658312395 + -1 t = 1.658312395 + -1 Combine like terms: 1.658312395 + -1 = 0.658312395 t = 0.658312395 Simplifying t = 0.658312395

Subproblem 2

t + 1 = -1.658312395 Simplifying t + 1 = -1.658312395 Reorder the terms: 1 + t = -1.658312395 Solving 1 + t = -1.658312395 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -1.658312395 + -1 Combine like terms: 1 + -1 = 0 0 + t = -1.658312395 + -1 t = -1.658312395 + -1 Combine like terms: -1.658312395 + -1 = -2.658312395 t = -2.658312395 Simplifying t = -2.658312395

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.658312395, -2.658312395}

Solution

t = {0.658312395, -2.658312395}

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