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Simplifying 4x2 + 15 = 9x2 + -6x Reorder the terms: 15 + 4x2 = 9x2 + -6x Reorder the terms: 15 + 4x2 = -6x + 9x2 Solving 15 + 4x2 = -6x + 9x2 Solving for variable 'x'. Reorder the terms: 15 + 6x + 4x2 + -9x2 = -6x + 9x2 + 6x + -9x2 Combine like terms: 4x2 + -9x2 = -5x2 15 + 6x + -5x2 = -6x + 9x2 + 6x + -9x2 Reorder the terms: 15 + 6x + -5x2 = -6x + 6x + 9x2 + -9x2 Combine like terms: -6x + 6x = 0 15 + 6x + -5x2 = 0 + 9x2 + -9x2 15 + 6x + -5x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 15 + 6x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3 + -1.2x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.2x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -1.2x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.2x + x2 = 0 + 3 -1.2x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.2x + x2 = 3 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 = 3 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 3 + 0.36 Combine like terms: 3 + 0.36 = 3.36 0.36 + -1.2x + x2 = 3.36 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 3.36 Calculate the square root of the right side: 1.833030278 Break this problem into two subproblems by setting (x + -0.6) equal to 1.833030278 and -1.833030278.Subproblem 1
x + -0.6 = 1.833030278 Simplifying x + -0.6 = 1.833030278 Reorder the terms: -0.6 + x = 1.833030278 Solving -0.6 + x = 1.833030278 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 = 1.833030278 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 1.833030278 + 0.6 x = 1.833030278 + 0.6 Combine like terms: 1.833030278 + 0.6 = 2.433030278 x = 2.433030278 Simplifying x = 2.433030278Subproblem 2
x + -0.6 = -1.833030278 Simplifying x + -0.6 = -1.833030278 Reorder the terms: -0.6 + x = -1.833030278 Solving -0.6 + x = -1.833030278 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 = -1.833030278 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -1.833030278 + 0.6 x = -1.833030278 + 0.6 Combine like terms: -1.833030278 + 0.6 = -1.233030278 x = -1.233030278 Simplifying x = -1.233030278Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.433030278, -1.233030278}
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