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Simplifying 3460 = 5x2 + 3x Reorder the terms: 3460 = 3x + 5x2 Solving 3460 = 3x + 5x2 Solving for variable 'x'. Reorder the terms: 3460 + -3x + -5x2 = 3x + -3x + 5x2 + -5x2 Combine like terms: 3x + -3x = 0 3460 + -3x + -5x2 = 0 + 5x2 + -5x2 3460 + -3x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 3460 + -3x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -692 + 0.6x + x2 = 0 Move the constant term to the right: Add '692' to each side of the equation. -692 + 0.6x + 692 + x2 = 0 + 692 Reorder the terms: -692 + 692 + 0.6x + x2 = 0 + 692 Combine like terms: -692 + 692 = 0 0 + 0.6x + x2 = 0 + 692 0.6x + x2 = 0 + 692 Combine like terms: 0 + 692 = 692 0.6x + x2 = 692 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 = 692 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 692 + 0.09 Combine like terms: 692 + 0.09 = 692.09 0.09 + 0.6x + x2 = 692.09 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 692.09 Calculate the square root of the right side: 26.307603464 Break this problem into two subproblems by setting (x + 0.3) equal to 26.307603464 and -26.307603464.Subproblem 1
x + 0.3 = 26.307603464 Simplifying x + 0.3 = 26.307603464 Reorder the terms: 0.3 + x = 26.307603464 Solving 0.3 + x = 26.307603464 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 = 26.307603464 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 26.307603464 + -0.3 x = 26.307603464 + -0.3 Combine like terms: 26.307603464 + -0.3 = 26.007603464 x = 26.007603464 Simplifying x = 26.007603464Subproblem 2
x + 0.3 = -26.307603464 Simplifying x + 0.3 = -26.307603464 Reorder the terms: 0.3 + x = -26.307603464 Solving 0.3 + x = -26.307603464 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 = -26.307603464 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -26.307603464 + -0.3 x = -26.307603464 + -0.3 Combine like terms: -26.307603464 + -0.3 = -26.607603464 x = -26.607603464 Simplifying x = -26.607603464Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.007603464, -26.607603464}
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