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Simplifying 5x2 = 3x + 6 Reorder the terms: 5x2 = 6 + 3x Solving 5x2 = 6 + 3x Solving for variable 'x'. Reorder the terms: -6 + -3x + 5x2 = 6 + 3x + -6 + -3x Reorder the terms: -6 + -3x + 5x2 = 6 + -6 + 3x + -3x Combine like terms: 6 + -6 = 0 -6 + -3x + 5x2 = 0 + 3x + -3x -6 + -3x + 5x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -6 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -0.6x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.6x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.6x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.6x + x2 = 0 + 1.2 -0.6x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -0.6x + x2 = 1.2 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 = 1.2 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 1.2 + 0.09 Combine like terms: 1.2 + 0.09 = 1.29 0.09 + -0.6x + x2 = 1.29 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 1.29 Calculate the square root of the right side: 1.135781669 Break this problem into two subproblems by setting (x + -0.3) equal to 1.135781669 and -1.135781669.Subproblem 1
x + -0.3 = 1.135781669 Simplifying x + -0.3 = 1.135781669 Reorder the terms: -0.3 + x = 1.135781669 Solving -0.3 + x = 1.135781669 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 = 1.135781669 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.135781669 + 0.3 x = 1.135781669 + 0.3 Combine like terms: 1.135781669 + 0.3 = 1.435781669 x = 1.435781669 Simplifying x = 1.435781669Subproblem 2
x + -0.3 = -1.135781669 Simplifying x + -0.3 = -1.135781669 Reorder the terms: -0.3 + x = -1.135781669 Solving -0.3 + x = -1.135781669 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 = -1.135781669 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.135781669 + 0.3 x = -1.135781669 + 0.3 Combine like terms: -1.135781669 + 0.3 = -0.835781669 x = -0.835781669 Simplifying x = -0.835781669Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.435781669, -0.835781669}
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