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Simplifying 5x2 + 6x = 180 Reorder the terms: 6x + 5x2 = 180 Solving 6x + 5x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 6x + 5x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -36 + 1.2x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 1.2x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 1.2x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 1.2x + x2 = 0 + 36 1.2x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 1.2x + x2 = 36 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 = 36 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 36 + 0.36 Combine like terms: 36 + 0.36 = 36.36 0.36 + 1.2x + x2 = 36.36 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 36.36 Calculate the square root of the right side: 6.029925373 Break this problem into two subproblems by setting (x + 0.6) equal to 6.029925373 and -6.029925373.Subproblem 1
x + 0.6 = 6.029925373 Simplifying x + 0.6 = 6.029925373 Reorder the terms: 0.6 + x = 6.029925373 Solving 0.6 + x = 6.029925373 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 = 6.029925373 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 6.029925373 + -0.6 x = 6.029925373 + -0.6 Combine like terms: 6.029925373 + -0.6 = 5.429925373 x = 5.429925373 Simplifying x = 5.429925373Subproblem 2
x + 0.6 = -6.029925373 Simplifying x + 0.6 = -6.029925373 Reorder the terms: 0.6 + x = -6.029925373 Solving 0.6 + x = -6.029925373 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 = -6.029925373 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -6.029925373 + -0.6 x = -6.029925373 + -0.6 Combine like terms: -6.029925373 + -0.6 = -6.629925373 x = -6.629925373 Simplifying x = -6.629925373Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.429925373, -6.629925373}
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