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Simplifying 5x2 + 6x = 70 Reorder the terms: 6x + 5x2 = 70 Solving 6x + 5x2 = 70 Solving for variable 'x'. Reorder the terms: -70 + 6x + 5x2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -14 + 1.2x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 1.2x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 1.2x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 1.2x + x2 = 0 + 14 1.2x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 1.2x + x2 = 14 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 14 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 14 + 0.36 Combine like terms: 14 + 0.36 = 14.36 0.36 + 1.2x + x2 = 14.36 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 14.36 Calculate the square root of the right side: 3.789459064 Break this problem into two subproblems by setting (x + 0.6) equal to 3.789459064 and -3.789459064.Subproblem 1
x + 0.6 = 3.789459064 Simplifying x + 0.6 = 3.789459064 Reorder the terms: 0.6 + x = 3.789459064 Solving 0.6 + x = 3.789459064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 3.789459064 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 3.789459064 + -0.6 x = 3.789459064 + -0.6 Combine like terms: 3.789459064 + -0.6 = 3.189459064 x = 3.189459064 Simplifying x = 3.189459064Subproblem 2
x + 0.6 = -3.789459064 Simplifying x + 0.6 = -3.789459064 Reorder the terms: 0.6 + x = -3.789459064 Solving 0.6 + x = -3.789459064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -3.789459064 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -3.789459064 + -0.6 x = -3.789459064 + -0.6 Combine like terms: -3.789459064 + -0.6 = -4.389459064 x = -4.389459064 Simplifying x = -4.389459064Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.189459064, -4.389459064}
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