240-70m=5m^2

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Solution for 240-70m=5m^2 equation:


Simplifying
240 + -70m = 5m2

Solving
240 + -70m = 5m2

Solving for variable 'm'.

Combine like terms: 5m2 + -5m2 = 0
240 + -70m + -5m2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(48 + -14m + -1m2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(48 + -14m + -1m2)' equal to zero and attempt to solve: Simplifying 48 + -14m + -1m2 = 0 Solving 48 + -14m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 14m + m2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 14m + 48 + m2 = 0 + 48 Reorder the terms: -48 + 48 + 14m + m2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 14m + m2 = 0 + 48 14m + m2 = 0 + 48 Combine like terms: 0 + 48 = 48 14m + m2 = 48 The m term is 14m. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14m + 49 + m2 = 48 + 49 Reorder the terms: 49 + 14m + m2 = 48 + 49 Combine like terms: 48 + 49 = 97 49 + 14m + m2 = 97 Factor a perfect square on the left side: (m + 7)(m + 7) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (m + 7) equal to 9.848857802 and -9.848857802.

Subproblem 1

m + 7 = 9.848857802 Simplifying m + 7 = 9.848857802 Reorder the terms: 7 + m = 9.848857802 Solving 7 + m = 9.848857802 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + m = 9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + m = 9.848857802 + -7 m = 9.848857802 + -7 Combine like terms: 9.848857802 + -7 = 2.848857802 m = 2.848857802 Simplifying m = 2.848857802

Subproblem 2

m + 7 = -9.848857802 Simplifying m + 7 = -9.848857802 Reorder the terms: 7 + m = -9.848857802 Solving 7 + m = -9.848857802 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + m = -9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + m = -9.848857802 + -7 m = -9.848857802 + -7 Combine like terms: -9.848857802 + -7 = -16.848857802 m = -16.848857802 Simplifying m = -16.848857802

Solution

The solution to the problem is based on the solutions from the subproblems. m = {2.848857802, -16.848857802}

Solution

m = {2.848857802, -16.848857802}

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