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Simplifying 5x2 + -3x = 15 Reorder the terms: -3x + 5x2 = 15 Solving -3x + 5x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -3x + 5x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + -0.6x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.6x + x2 = 0 + 3 -0.6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.6x + x2 = 3 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 3 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 3 + 0.09 Combine like terms: 3 + 0.09 = 3.09 0.09 + -0.6x + x2 = 3.09 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 3.09 Calculate the square root of the right side: 1.757839583 Break this problem into two subproblems by setting (x + -0.3) equal to 1.757839583 and -1.757839583.Subproblem 1
x + -0.3 = 1.757839583 Simplifying x + -0.3 = 1.757839583 Reorder the terms: -0.3 + x = 1.757839583 Solving -0.3 + x = 1.757839583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.757839583 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.757839583 + 0.3 x = 1.757839583 + 0.3 Combine like terms: 1.757839583 + 0.3 = 2.057839583 x = 2.057839583 Simplifying x = 2.057839583Subproblem 2
x + -0.3 = -1.757839583 Simplifying x + -0.3 = -1.757839583 Reorder the terms: -0.3 + x = -1.757839583 Solving -0.3 + x = -1.757839583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.757839583 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.757839583 + 0.3 x = -1.757839583 + 0.3 Combine like terms: -1.757839583 + 0.3 = -1.457839583 x = -1.457839583 Simplifying x = -1.457839583Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.057839583, -1.457839583}
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